# OpenStax University Physics/Archived sample/Exams

PhysicsCalc2152657831440
Sample page for instructor to print out as a pff file. Version V0 is for the instructor's eyes only. V1 and V2 are to be released only on the day of each test.
Since this takes 98 pages to print, I have recently modified the program so that I can print out each test individually.

### PhysicsCalc2:T1:V0

PhysicsCalc2152657831440
1) Integrate the line integral of ${\vec {F}}=2xy{\hat {x}}+7.2x{\hat {y}}$ from the origin to the point at x = 2.4 and y = 3.2
    a) 3.05E+01
    b) 3.26E+01
    c) 3.49E+01
    d) 3.73E+01
    e) 3.99E+01
2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a$^2$, where β equals
    a) 3.38 x 10$^{-3}$ unit
    b) 4.1 x 10$^{-3}$ unit
    c) 4.96 x 10$^{-3}$ unit
    d) 6.01 x 10$^{-3}$ unit
    e) 7.28 x 10$^{-3}$ unit
3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a$^2$, where β equals
    a) 2.36 x 10$^{-1}$ unit
    b) 2.86 x 10$^{-1}$ unit
    c) 3.47 x 10$^{-1}$ unit
    d) 4.2 x 10$^{-1}$ unit
    e) 5.09 x 10$^{-1}$ unit
4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    a) 7−s
    b) 3−s
    c) s−7
    d) 8
    e) s−3
5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    a) 1−s
    b) s−4
    c) 5
    d) 5−s
    e) s−1
6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:
    a) 2/3
    b) 1/2
    c) 2
    d) 3
    e) 3/2
7) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the force between the plates if they are 0.6 mm apart?
    a) 412 N.
    b) 474 N.
    c) 545 N.
    d) 626 N.
    e) 720 N.
8) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the energy stored in the capacitor if the plates are 0.6 mm apart?
    a) 0.38 J.
    b) 0.43 J.
    c) 0.5 J.
    d) 0.57 J.
    e) 0.66 J.
9) How fast is a 2952 eV electron moving?
    a) 6.4 x 10$^6$ m/s.
    b) 9.5 x 10$^6$ m/s.
    c) 1.4 x 10$^7$ m/s.
    d) 2.1 x 10$^7$ m/s.
    e) 3.2 x 10$^7$ m/s.
10) A proton is accellerated (at rest) from a plate held at 729.8 volts to a plate at zero volts. What is the final speed?
    a) 1.7 x 10$^5$ m/s.
    b) 2.5 x 10$^5$ m/s.
    c) 3.7 x 10$^5$ m/s.
    d) 5.6 x 10$^5$ m/s.
    e) 8.4 x 10$^5$ m/s.
11) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the curved side surface of the cylinder.
    a) 9.205E+02
    b) 1.115E+03
    c) 1.351E+03
    d) 1.637E+03
    e) 1.983E+03
12) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    a) 3.417E+03
    b) 4.140E+03
    c) 5.016E+03
    d) 6.077E+03
    e) 7.362E+03

### KEY:PhysicsCalc2:T1:V0

PhysicsCalc2152657831440
1) Integrate the line integral of ${\vec {F}}=2xy{\hat {x}}+7.2x{\hat {y}}$ from the origin to the point at x = 2.4 and y = 3.2
    -a) 3.05E+01
    -b) 3.26E+01
    -c) 3.49E+01
    -d) 3.73E+01
    +e) 3.99E+01
2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a$^2$, where β equals
    -a) 3.38 x 10$^{-3}$ unit
    -b) 4.1 x 10$^{-3}$ unit
    -c) 4.96 x 10$^{-3}$ unit
    -d) 6.01 x 10$^{-3}$ unit
    +e) 7.28 x 10$^{-3}$ unit
3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a$^2$, where β equals
    -a) 2.36 x 10$^{-1}$ unit
    -b) 2.86 x 10$^{-1}$ unit
    +c) 3.47 x 10$^{-1}$ unit
    -d) 4.2 x 10$^{-1}$ unit
    -e) 5.09 x 10$^{-1}$ unit
4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    +a) 7−s
    -b) 3−s
    -c) s−7
    -d) 8
    -e) s−3
5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    +a) 1−s
    -b) s−4
    -c) 5
    -d) 5−s
    -e) s−1
6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:
    -a) 2/3
    -b) 1/2
    -c) 2
    -d) 3
    +e) 3/2
7) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the force between the plates if they are 0.6 mm apart?
    -a) 412 N.
    -b) 474 N.
    -c) 545 N.
    -d) 626 N.
    +e) 720 N.
8) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the energy stored in the capacitor if the plates are 0.6 mm apart?
    -a) 0.38 J.
    +b) 0.43 J.
    -c) 0.5 J.
    -d) 0.57 J.
    -e) 0.66 J.
9) How fast is a 2952 eV electron moving?
    -a) 6.4 x 10$^6$ m/s.
    -b) 9.5 x 10$^6$ m/s.
    -c) 1.4 x 10$^7$ m/s.
    -d) 2.1 x 10$^7$ m/s.
    +e) 3.2 x 10$^7$ m/s.
10) A proton is accellerated (at rest) from a plate held at 729.8 volts to a plate at zero volts. What is the final speed?
    -a) 1.7 x 10$^5$ m/s.
    -b) 2.5 x 10$^5$ m/s.
    +c) 3.7 x 10$^5$ m/s.
    -d) 5.6 x 10$^5$ m/s.
    -e) 8.4 x 10$^5$ m/s.
11) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the curved side surface of the cylinder.
    -a) 9.205E+02
    -b) 1.115E+03
    +c) 1.351E+03
    -d) 1.637E+03
    -e) 1.983E+03
12) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    -a) 3.417E+03
    -b) 4.140E+03
    -c) 5.016E+03
    +d) 6.077E+03
    -e) 7.362E+03

### PhysicsCalc2:T1:V1

PhysicsCalc2152657831440
1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2+1.45z)\rho ^{2}{\hat {\rho }}+8.02z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the curved side surface of the cylinder.
    a) 4.021E+02
    b) 4.872E+02
    c) 5.902E+02
    d) 7.151E+02
    e) 8.663E+02
2) A 0.5 Farad capacitor charged with 1.6 Coulombs. What is the energy stored in the capacitor if the plates are 0.7 mm apart?
    a) 2.23 J.
    b) 2.56 J.
    c) 2.94 J.
    d) 3.39 J.
    e) 3.89 J.
3) A proton is accellerated (at rest) from a plate held at 767.8 volts to a plate at zero volts. What is the final speed?
    a) 1.1 x 10$^5$ m/s.
    b) 1.7 x 10$^5$ m/s.
    c) 2.6 x 10$^5$ m/s.
    d) 3.8 x 10$^5$ m/s.
    e) 5.8 x 10$^5$ m/s.
4) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?
    a) 1826 N.
    b) 2099 N.
    c) 2414 N.
    d) 2776 N.
    e) 3193 N.
5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a$^2$, where β equals
    a) 2.86 x 10$^{-1}$ unit
    b) 3.47 x 10$^{-1}$ unit
    c) 4.2 x 10$^{-1}$ unit
    d) 5.09 x 10$^{-1}$ unit
    e) 6.17 x 10$^{-1}$ unit
6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:
    a) 1/2
    b) 2
    c) 2/3
    d) 3
    e) 3/2
7) How fast is a 2663 eV electron moving?
    a) 3.1 x 10$^7$ m/s.
    b) 4.6 x 10$^7$ m/s.
    c) 6.9 x 10$^7$ m/s.
    d) 1 x 10$^8$ m/s.
    e) 1.5 x 10$^8$ m/s.
8) Integrate the line integral of ${\vec {F}}=4xy{\hat {x}}+9.8x{\hat {y}}$ from the origin to the point at x = 2.6 and y = 3.9
    a) 7.93E+01
    b) 8.48E+01
    c) 9.08E+01
    d) 9.71E+01
    e) 1.04E+02
9) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(1.88+1.29z)\rho ^{2}{\hat {\rho }}+7.2z^{2}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    a) 1.248E+03
    b) 1.512E+03
    c) 1.832E+03
    d) 2.220E+03
    e) 2.689E+03
10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    a) s−4
    b) 5−s
    c) 5
    d) 1−s
    e) s−1
11) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 4a) is βkQ/a$^2$, where β equals
    a) 1.76 x 10$^{-3}$ unit
    b) 2.13 x 10$^{-3}$ unit
    c) 2.59 x 10$^{-3}$ unit
    d) 3.13 x 10$^{-3}$ unit
    e) 3.79 x 10$^{-3}$ unit
12) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    a) 8
    b) s−3
    c) 3−s
    d) s−7
    e) 7−s

### KEY:PhysicsCalc2:T1:V1

PhysicsCalc2152657831440
1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2+1.45z)\rho ^{2}{\hat {\rho }}+8.02z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the curved side surface of the cylinder.
    +a) 4.021E+02
    -b) 4.872E+02
    -c) 5.902E+02
    -d) 7.151E+02
    -e) 8.663E+02
2) A 0.5 Farad capacitor charged with 1.6 Coulombs. What is the energy stored in the capacitor if the plates are 0.7 mm apart?
    -a) 2.23 J.
    +b) 2.56 J.
    -c) 2.94 J.
    -d) 3.39 J.
    -e) 3.89 J.
3) A proton is accellerated (at rest) from a plate held at 767.8 volts to a plate at zero volts. What is the final speed?
    -a) 1.1 x 10$^5$ m/s.
    -b) 1.7 x 10$^5$ m/s.
    -c) 2.6 x 10$^5$ m/s.
    +d) 3.8 x 10$^5$ m/s.
    -e) 5.8 x 10$^5$ m/s.
4) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?
    -a) 1826 N.
    -b) 2099 N.
    +c) 2414 N.
    -d) 2776 N.
    -e) 3193 N.
5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a$^2$, where β equals
    -a) 2.86 x 10$^{-1}$ unit
    +b) 3.47 x 10$^{-1}$ unit
    -c) 4.2 x 10$^{-1}$ unit
    -d) 5.09 x 10$^{-1}$ unit
    -e) 6.17 x 10$^{-1}$ unit
6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:
    -a) 1/2
    -b) 2
    -c) 2/3
    -d) 3
    +e) 3/2
7) How fast is a 2663 eV electron moving?
    +a) 3.1 x 10$^7$ m/s.
    -b) 4.6 x 10$^7$ m/s.
    -c) 6.9 x 10$^7$ m/s.
    -d) 1 x 10$^8$ m/s.
    -e) 1.5 x 10$^8$ m/s.
8) Integrate the line integral of ${\vec {F}}=4xy{\hat {x}}+9.8x{\hat {y}}$ from the origin to the point at x = 2.6 and y = 3.9
    -a) 7.93E+01
    +b) 8.48E+01
    -c) 9.08E+01
    -d) 9.71E+01
    -e) 1.04E+02
9) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(1.88+1.29z)\rho ^{2}{\hat {\rho }}+7.2z^{2}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    -a) 1.248E+03
    -b) 1.512E+03
    +c) 1.832E+03
    -d) 2.220E+03
    -e) 2.689E+03
10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    -a) s−4
    -b) 5−s
    -c) 5
    +d) 1−s
    -e) s−1
11) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 4a) is βkQ/a$^2$, where β equals
    -a) 1.76 x 10$^{-3}$ unit
    -b) 2.13 x 10$^{-3}$ unit
    -c) 2.59 x 10$^{-3}$ unit
    +d) 3.13 x 10$^{-3}$ unit
    -e) 3.79 x 10$^{-3}$ unit
12) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    -a) 8
    -b) s−3
    -c) 3−s
    -d) s−7
    +e) 7−s

### PhysicsCalc2:T1:V2

PhysicsCalc2152657831440
1) A proton is accelerated (at rest) from a plate held at 333.6 volts to a plate at zero volts. What is the final speed?
    a) 1.1 x 10$^5$ m/s.
    b) 1.7 x 10$^5$ m/s.
    c) 2.5 x 10$^5$ m/s.
    d) 3.8 x 10$^5$ m/s.
    e) 5.7 x 10$^5$ m/s.
2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 4a) is βkQ/a$^2$, where β equals
    a) 1.76 x 10$^{-3}$ unit
    b) 2.13 x 10$^{-3}$ unit
    c) 2.59 x 10$^{-3}$ unit
    d) 3.13 x 10$^{-3}$ unit
    e) 3.79 x 10$^{-3}$ unit
3) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the energy stored in the capacitor if the plates are 0.3 mm apart?
    a) 0.91 J.
    b) 1.05 J.
    c) 1.21 J.
    d) 1.39 J.
    e) 1.6 J.
4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    a) 5
    b) 1−s
    c) 5−s
    d) s−1
    e) s−4
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    a) 6.201E+02
    b) 7.513E+02
    c) 9.102E+02
    d) 1.103E+03
    e) 1.336E+03
6) How fast is a 2355 eV electron moving?
    a) 1.9 x 10$^7$ m/s.
    b) 2.9 x 10$^7$ m/s.
    c) 4.3 x 10$^7$ m/s.
    d) 6.5 x 10$^7$ m/s.
    e) 9.7 x 10$^7$ m/s.
7) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?
    a) 1826 N.
    b) 2099 N.
    c) 2414 N.
    d) 2776 N.
    e) 3193 N.
8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a$^2$, where β equals
    a) 2.86 x 10$^{-1}$
    b) 3.47 x 10$^{-1}$
    c) 4.2 x 10$^{-1}$
    d) 5.09 x 10$^{-1}$
    e) 6.17 x 10$^{-1}$
9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    a) s−7
    b) 8
    c) s−3
    d) 7−s
    e) 3−s
10) Integrate the line integral of ${\vec {F}}=2xy{\hat {x}}+9.7x{\hat {y}}$ from the origin to the point at x = 2.8 and y = 3.2
    a) 5.26E+01
    b) 5.62E+01
    c) 6.02E+01
    d) 6.44E+01
    e) 6.89E+01
11) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:
    a) 2
    b) 1/2
    c) 3
    d) 2/3
    e) 3/2
12) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the curved side surface of the cylinder.
    a) 7.465E+02
    b) 9.044E+02
    c) 1.096E+03
    d) 1.327E+03
    e) 1.608E+03

### KEY:PhysicsCalc2:T1:V2

PhysicsCalc2152657831440
1) A proton is accelerated (at rest) from a plate held at 333.6 volts to a plate at zero volts. What is the final speed?
    -a) 1.1 x 10$^5$ m/s.
    -b) 1.7 x 10$^5$ m/s.
    +c) 2.5 x 10$^5$ m/s.
    -d) 3.8 x 10$^5$ m/s.
    -e) 5.7 x 10$^5$ m/s.
2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 4a) is βkQ/a$^2$, where β equals
    -a) 1.76 x 10$^{-3}$ unit
    -b) 2.13 x 10$^{-3}$ unit
    -c) 2.59 x 10$^{-3}$ unit
    +d) 3.13 x 10$^{-3}$ unit
    -e) 3.79 x 10$^{-3}$ unit
3) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the energy stored in the capacitor if the plates are 0.3 mm apart?
    -a) 0.91 J.
    -b) 1.05 J.
    -c) 1.21 J.
    +d) 1.39 J.
    -e) 1.6 J.
4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    -a) 5
    +b) 1−s
    -c) 5−s
    -d) s−1
    -e) s−4
5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    -a) 6.201E+02
    -b) 7.513E+02
    -c) 9.102E+02
    +d) 1.103E+03
    -e) 1.336E+03
6) How fast is a 2355 eV electron moving?
    -a) 1.9 x 10$^7$ m/s.
    +b) 2.9 x 10$^7$ m/s.
    -c) 4.3 x 10$^7$ m/s.
    -d) 6.5 x 10$^7$ m/s.
    -e) 9.7 x 10$^7$ m/s.
7) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?
    -a) 1826 N.
    -b) 2099 N.
    +c) 2414 N.
    -d) 2776 N.
    -e) 3193 N.
8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a$^2$, where β equals
    -a) 2.86 x 10$^{-1}$
    +b) 3.47 x 10$^{-1}$
    -c) 4.2 x 10$^{-1}$
    -d) 5.09 x 10$^{-1}$
    -e) 6.17 x 10$^{-1}$
9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:
    -a) s−7
    -b) 8
    -c) s−3
    +d) 7−s
    -e) 3−s
10) Integrate the line integral of ${\vec {F}}=2xy{\hat {x}}+9.7x{\hat {y}}$ from the origin to the point at x = 2.8 and y = 3.2
    -a) 5.26E+01
    -b) 5.62E+01
    +c) 6.02E+01
    -d) 6.44E+01
    -e) 6.89E+01
11) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:
    -a) 2
    -b) 1/2
    -c) 3
    -d) 2/3
    +e) 3/2
12) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the curved side surface of the cylinder.
    -a) 7.465E+02
    -b) 9.044E+02
    -c) 1.096E+03
    -d) 1.327E+03
    +e) 1.608E+03

### PhysicsCalc2:T2:V0

PhysicsCalc2152657831440
1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    b) $2R\varepsilon _{0}E=r^{2}\rho$
    c) $2r\varepsilon _{0}E=R^{2}\rho$
    d) none of these are correct
    e) $2\varepsilon _{0}E=r\rho$
2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?
    a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
    b) none of these are correct
    c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?
    a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    b) none of these are correct
    c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
4) The diameter of a copper wire is 9.2 mm, and it carries a current of 64 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    a) 4.91 x 10$^{-5}$m/s
    b) 5.95 x 10$^{-5}$m/s
    c) 7.2 x 10$^{-5}$m/s
    d) 8.73 x 10$^{-5}$m/s
    e) 1.06 x 10$^{-4}$m/s
5) A power supply delivers 138 watts of power to a 206 ohm resistor. What was the applied voltage?
    a) 1.39 x 10$^2$ volts
    b) 1.69 x 10$^2$ volts
    c) 2.04 x 10$^2$ volts
    d) 2.47 x 10$^2$ volts
    e) 3 x 10$^2$ volts
6) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?
    a) None of these are true.
    b) $4.5\Omega .$
    c) $3.5\Omega .$
    d) $2.5\Omega .$
7) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?
    a) 2A
    b) 1.5A
    c) 3A
    d) 12A
8) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?
    a) 25 Joules
    b) None of these are true
    c) 5 Joules
    d) 3 Joules
9) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?
    a) None of these are true.
    b) $R_{1}=150V$ and $R_{2}=100V$.
    c) $R_{1}=125V$ and $R_{2}=125V$.
    d) $R_{1}=250V$ and $R_{2}=0V$.
10) Two resistors are in parallel with a voltage source. How do their voltages compare?
    a) None of these are true.
    b) The voltage across both resistors is half the voltage of the source.
    c) The voltage across both resistors is the same as the source.
    d) One has full voltage, the other has none.
11) A 6.4 ohm resistor is connected in series to a pair of 7.4 ohm resistors that are in parallel. What is the net resistance?
    a) 10.1 ohms.
    b) 11.6 ohms.
    c) 13.4 ohms.
    d) 15.4 ohms.
    e) 17.7 ohms.
12) A battery has an emf of 7.8 volts, and an internal resistance of 351 $k\Omega$. It is connected to a 4.2 $M\Omega$ resistor. What power is developed in the 4.2 $M\Omega$ resistor?
    a) 12.34 $\mu$W.
    b) 14.19 $\mu$W.
    c) 16.32 $\mu$W.
    d) 18.76 $\mu$W.
    e) 21.58 $\mu$W.

### KEY:PhysicsCalc2:T2:V0

PhysicsCalc2152657831440
1) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    -a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    -b) $2R\varepsilon _{0}E=r^{2}\rho$
    +c) $2r\varepsilon _{0}E=R^{2}\rho$
    -d) none of these are correct
    -e) $2\varepsilon _{0}E=r\rho$
2) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?
    -a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
    -b) none of these are correct
    -c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    -d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    +e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?
    -a) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    -b) none of these are correct
    +c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    -d) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    -e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
4) The diameter of a copper wire is 9.2 mm, and it carries a current of 64 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    -a) 4.91 x 10$^{-5}$m/s
    -b) 5.95 x 10$^{-5}$m/s
    +c) 7.2 x 10$^{-5}$m/s
    -d) 8.73 x 10$^{-5}$m/s
    -e) 1.06 x 10$^{-4}$m/s
5) A power supply delivers 138 watts of power to a 206 ohm resistor. What was the applied voltage?
    -a) 1.39 x 10$^2$ volts
    +b) 1.69 x 10$^2$ volts
    -c) 2.04 x 10$^2$ volts
    -d) 2.47 x 10$^2$ volts
    -e) 3 x 10$^2$ volts
6) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?
    -a) None of these are true.
    -b) $4.5\Omega .$
    -c) $3.5\Omega .$
    +d) $2.5\Omega .$
7) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?
    +a) 2A
    -b) 1.5A
    -c) 3A
    -d) 12A
8) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?
    +a) 25 Joules
    -b) None of these are true
    -c) 5 Joules
    -d) 3 Joules
9) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?
    -a) None of these are true.
    -b) $R_{1}=150V$ and $R_{2}=100V$.
    +c) $R_{1}=125V$ and $R_{2}=125V$.
    -d) $R_{1}=250V$ and $R_{2}=0V$.
10) Two resistors are in parallel with a voltage source. How do their voltages compare?
    -a) None of these are true.
    -b) The voltage across both resistors is half the voltage of the source.
    +c) The voltage across both resistors is the same as the source.
    -d) One has full voltage, the other has none.
11) A 6.4 ohm resistor is connected in series to a pair of 7.4 ohm resistors that are in parallel. What is the net resistance?
    +a) 10.1 ohms.
    -b) 11.6 ohms.
    -c) 13.4 ohms.
    -d) 15.4 ohms.
    -e) 17.7 ohms.
12) A battery has an emf of 7.8 volts, and an internal resistance of 351 $k\Omega$. It is connected to a 4.2 $M\Omega$ resistor. What power is developed in the 4.2 $M\Omega$ resistor?
    +a) 12.34 $\mu$W.
    -b) 14.19 $\mu$W.
    -c) 16.32 $\mu$W.
    -d) 18.76 $\mu$W.
    -e) 21.58 $\mu$W.

### PhysicsCalc2:T2:V1

PhysicsCalc2152657831440
1) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?
    a) None of these are true.
    b) $4.5\Omega .$
    c) $2.5\Omega .$
    d) $3.5\Omega .$
2) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?
    a) 3A
    b) 2A
    c) 1.5A
    d) 12A
3) A power supply delivers 169 watts of power to a 219 ohm resistor. What was the applied voltage?
    a) 8.93 x 10$^1$ volts
    b) 1.08 x 10$^2$ volts
    c) 1.31 x 10$^2$ volts
    d) 1.59 x 10$^2$ volts
    e) 1.92 x 10$^2$ volts
4) A 5.6 ohm resistor is connected in series to a pair of 7.2 ohm resistors that are in parallel. What is the net resistance?
    a) 7 ohms.
    b) 8 ohms.
    c) 9.2 ohms.
    d) 10.6 ohms.
    e) 12.2 ohms.
5) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?
    a) none of these are correct
    b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    a) none of these are correct
    b) $2R\varepsilon _{0}E=r^{2}\rho$
    c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    d) $2r\varepsilon _{0}E=R^{2}\rho$
    e) $2\varepsilon _{0}E=r\rho$
7) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?
    a) 5 Joules
    b) 25 Joules
    c) None of these are true
    d) 3 Joules
8) A battery has an emf of 6.5 volts, and an internal resistance of 244 $k\Omega$. It is connected to a 4 $M\Omega$ resistor. What power is developed in the 4 $M\Omega$ resistor?
    a) 7.09 $\mu$W.
    b) 8.16 $\mu$W.
    c) 9.38 $\mu$W.
    d) 10.79 $\mu$W.
    e) 12.41 $\mu$W.
9) The diameter of a copper wire is 7.4 mm, and it carries a current of 38 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    a) 3.07 x 10$^{-5}$m/s
    b) 3.72 x 10$^{-5}$m/s
    c) 4.5 x 10$^{-5}$m/s
    d) 5.46 x 10$^{-5}$m/s
    e) 6.61 x 10$^{-5}$m/s
10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?
    a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    d) none of these are correct
    e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
11) Two resistors are in parallel with a voltage source. How do their voltages compare?
    a) None of these are true.
    b) The voltage across both resistors is the same as the source.
    c) One has full voltage, the other has none.
    d) The voltage across both resistors is half the voltage of the source.
12) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?
    a) $R_{1}=150V$ and $R_{2}=100V$.
    b) $R_{1}=250V$ and $R_{2}=0V$.
    c) $R_{1}=125V$ and $R_{2}=125V$.
    d) None of these are true.

### KEY:PhysicsCalc2:T2:V1

PhysicsCalc2152657831440
1) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?
    -a) None of these are true.
    -b) $4.5\Omega .$
    +c) $2.5\Omega .$
    -d) $3.5\Omega .$
2) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?
    -a) 3A
    +b) 2A
    -c) 1.5A
    -d) 12A
3) A power supply delivers 169 watts of power to a 219 ohm resistor. What was the applied voltage?
    -a) 8.93 x 10$^1$ volts
    -b) 1.08 x 10$^2$ volts
    -c) 1.31 x 10$^2$ volts
    -d) 1.59 x 10$^2$ volts
    +e) 1.92 x 10$^2$ volts
4) A 5.6 ohm resistor is connected in series to a pair of 7.2 ohm resistors that are in parallel. What is the net resistance?
    -a) 7 ohms.
    -b) 8 ohms.
    +c) 9.2 ohms.
    -d) 10.6 ohms.
    -e) 12.2 ohms.
5) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?
    -a) none of these are correct
    -b) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    +c) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    -d) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    -e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
6) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    -a) none of these are correct
    -b) $2R\varepsilon _{0}E=r^{2}\rho$
    -c) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    +d) $2r\varepsilon _{0}E=R^{2}\rho$
    -e) $2\varepsilon _{0}E=r\rho$
7) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?
    -a) 5 Joules
    +b) 25 Joules
    -c) None of these are true
    -d) 3 Joules
8) A battery has an emf of 6.5 volts, and an internal resistance of 244 $k\Omega$. It is connected to a 4 $M\Omega$ resistor. What power is developed in the 4 $M\Omega$ resistor?
    -a) 7.09 $\mu$W.
    -b) 8.16 $\mu$W.
    +c) 9.38 $\mu$W.
    -d) 10.79 $\mu$W.
    -e) 12.41 $\mu$W.
9) The diameter of a copper wire is 7.4 mm, and it carries a current of 38 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    -a) 3.07 x 10$^{-5}$m/s
    -b) 3.72 x 10$^{-5}$m/s
    -c) 4.5 x 10$^{-5}$m/s
    -d) 5.46 x 10$^{-5}$m/s
    +e) 6.61 x 10$^{-5}$m/s
10) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?
    -a) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    +b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    -c) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    -d) none of these are correct
    -e) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
11) Two resistors are in parallel with a voltage source. How do their voltages compare?
    -a) None of these are true.
    +b) The voltage across both resistors is the same as the source.
    -c) One has full voltage, the other has none.
    -d) The voltage across both resistors is half the voltage of the source.
12) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?
    -a) $R_{1}=150V$ and $R_{2}=100V$.
    -b) $R_{1}=250V$ and $R_{2}=0V$.
    +c) $R_{1}=125V$ and $R_{2}=125V$.
    -d) None of these are true.

### PhysicsCalc2:T2:V2

PhysicsCalc2152657831440
1) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?
    a) None of these are true.
    b) $R_{1}=150V$ and $R_{2}=100V$.
    c) $R_{1}=250V$ and $R_{2}=0V$.
    d) $R_{1}=125V$ and $R_{2}=125V$.
2) Two resistors are in parallel with a voltage source. How do their voltages compare?
    a) One has full voltage, the other has none.
    b) The voltage across both resistors is the same as the source.
    c) None of these are true.
    d) The voltage across both resistors is half the voltage of the source.
3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?
    a) none of these are correct
    b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
    d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
4) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?
    a) 25 Joules
    b) 3 Joules
    c) None of these are true
    d) 5 Joules
5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    a) $2R\varepsilon _{0}E=r^{2}\rho$
    b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    c) $2r\varepsilon _{0}E=R^{2}\rho$
    d) $2\varepsilon _{0}E=r\rho$
    e) none of these are correct
6) A battery has an emf of 5.6 volts, and an internal resistance of 295 $k\Omega$. It is connected to a 4.1 $M\Omega$ resistor. What power is developed in the 4.1 $M\Omega$ resistor?
    a) 3.81 $\mu$W.
    b) 4.38 $\mu$W.
    c) 5.03 $\mu$W.
    d) 5.79 $\mu$W.
    e) 6.66 $\mu$W.
7) The diameter of a copper wire is 7.4 mm, and it carries a current of 38 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    a) 3.07 x 10$^{-5}$m/s
    b) 3.72 x 10$^{-5}$m/s
    c) 4.5 x 10$^{-5}$m/s
    d) 5.46 x 10$^{-5}$m/s
    e) 6.61 x 10$^{-5}$m/s
8) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?
    a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
    b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    e) none of these are correct
9) A 5.8 ohm resistor is connected in series to a pair of 2.8 ohm resistors that are in parallel. What is the net resistance?
    a) 7.2 ohms.
    b) 8.3 ohms.
    c) 9.5 ohms.
    d) 11 ohms.
    e) 12.6 ohms.
10) A power supply delivers 101 watts of power to a 219 ohm resistor. What was the applied voltage?
    a) 1.49 x 10$^2$ volts
    b) 1.8 x 10$^2$ volts
    c) 2.18 x 10$^2$ volts
    d) 2.64 x 10$^2$ volts
    e) 3.2 x 10$^2$ volts
11) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?
    a) 1.5A
    b) 2A
    c) 12A
    d) 3A
12) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?
    a) $4.5\Omega .$
    b) None of these are true.
    c) $2.5\Omega .$
    d) $3.5\Omega .$

### KEY:PhysicsCalc2:T2:V2

PhysicsCalc2152657831440
1) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?
    -a) None of these are true.
    -b) $R_{1}=150V$ and $R_{2}=100V$.
    -c) $R_{1}=250V$ and $R_{2}=0V$.
    +d) $R_{1}=125V$ and $R_{2}=125V$.
2) Two resistors are in parallel with a voltage source. How do their voltages compare?
    -a) One has full voltage, the other has none.
    +b) The voltage across both resistors is the same as the source.
    -c) None of these are true.
    -d) The voltage across both resistors is half the voltage of the source.
3) A sphere has a uniform charge density of $\rho$, and a radius equal to R. What formula describes the electric field at a distance r < R?
    -a) none of these are correct
    +b) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    -c) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
    -d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    -e) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
4) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?
    +a) 25 Joules
    -b) 3 Joules
    -c) None of these are true
    -d) 5 Joules
5) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    -a) $2R\varepsilon _{0}E=r^{2}\rho$
    -b) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    +c) $2r\varepsilon _{0}E=R^{2}\rho$
    -d) $2\varepsilon _{0}E=r\rho$
    -e) none of these are correct
6) A battery has an emf of 5.6 volts, and an internal resistance of 295 $k\Omega$. It is connected to a 4.1 $M\Omega$ resistor. What power is developed in the 4.1 $M\Omega$ resistor?
    -a) 3.81 $\mu$W.
    -b) 4.38 $\mu$W.
    -c) 5.03 $\mu$W.
    -d) 5.79 $\mu$W.
    +e) 6.66 $\mu$W.
7) The diameter of a copper wire is 7.4 mm, and it carries a current of 38 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    -a) 3.07 x 10$^{-5}$m/s
    -b) 3.72 x 10$^{-5}$m/s
    -c) 4.5 x 10$^{-5}$m/s
    -d) 5.46 x 10$^{-5}$m/s
    +e) 6.61 x 10$^{-5}$m/s
8) A sphere has a uniform charge density of $\rho$, and a radius or R. What formula describes the electric field at a distance r > R?
    -a) $r^{2}\varepsilon _{0}E=r^{3}\rho /2$
    +b) $r^{2}\varepsilon _{0}E=R^{3}\rho /3$
    -c) $r^{2}\varepsilon _{0}E=r^{3}\rho /3$
    -d) $r^{2}\varepsilon _{0}E=R^{3}\rho /2$
    -e) none of these are correct
9) A 5.8 ohm resistor is connected in series to a pair of 2.8 ohm resistors that are in parallel. What is the net resistance?
    +a) 7.2 ohms.
    -b) 8.3 ohms.
    -c) 9.5 ohms.
    -d) 11 ohms.
    -e) 12.6 ohms.
10) A power supply delivers 101 watts of power to a 219 ohm resistor. What was the applied voltage?
    +a) 1.49 x 10$^2$ volts
    -b) 1.8 x 10$^2$ volts
    -c) 2.18 x 10$^2$ volts
    -d) 2.64 x 10$^2$ volts
    -e) 3.2 x 10$^2$ volts
11) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?
    -a) 1.5A
    +b) 2A
    -c) 12A
    -d) 3A
12) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?
    -a) $4.5\Omega .$
    -b) None of these are true.
    +c) $2.5\Omega .$
    -d) $3.5\Omega .$

### PhysicsCalc2:T3:V0

PhysicsCalc2152657831440
1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:
    a) 9$^2$ + (2-s)$^2$
    b) 9$^2$ + (7-s)$^2$
    c) 7$^2$ + (2-s)$^2$
    d) 2$^2$ + (9-s)$^2$
    e) 2$^2$ + (7-s)$^2$
2) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?
    a) 11.67 Joules
    b) 2.5 Watts
    c) 1.67 Watts
    d) None of these are ture.
3) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e$^3$? (where e =2.7...)
    a) 1.88 x 10$^9$ s.
    b) 5.93 x 10$^9$ s.
    c) 1.88 x 10$^{10}$ s.
    d) 5.93 x 10$^{10}$ s.
    e) 1.88 x 10$^{11}$ s.
4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
    a) 5.14 x 10$^{-5}$ Volts
    b) 1.62 x 10$^{-4}$ Volts
    c) 5.14 x 10$^{-4}$ Volts
    d) 1.62 x 10$^{-3}$ Volts
    e) 5.14 x 10$^{-3}$ Volts
5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?
    a) 1.1 x 10$^0$ volts
    b) 3.6 x 10$^0$ volts
    c) 1.1 x 10$^1$ volts
    d) 3.6 x 10$^1$ volts
    e) 1.1 x 10$^2$ volts
6) An loop of wire with 54 turns has a radius of 0.8 meters, and is oriented with its axis parallel to a magetic field of 0.86 Tesla. What is the induced voltage if this field is reduced to 46% of its original value in 2.4 seconds?
    a) 1.43 x 10$^1$ volts
    b) 1.73 x 10$^1$ volts
    c) 2.1 x 10$^1$ volts
    d) 2.55 x 10$^1$ volts
    e) 3.08 x 10$^1$ volts
7) An important principle that allows fiber optics to work is
    a) the invariance of the speed of light
    b) total internal reflection
    c) the Doppler shift
    d) partial internal absorption
    e) total external refraction
8) The focal point is where
    a) rays meet if they were parallel to the optical axis before striking a lens
    b) rays meet whenever they are forming an image
    c) rays meet whenever they pass through a lens
    d) the center of the lens
    e) rays meet if they are parallel to each other
9) The law of reflection applies to
    a) both flat and curved surfaces
    b) flat surfaces
    c) curved surfaces
    d) telescopes but not microscopes
    e) only light in a vacuum
10) In optics, normal means
    a) to the right of the optical axis
    b) to the left of the optical axis
    c) perpendicular to the surface
    d) parallel to the surface
11) An object of height 0.75 cm is placed 147 cm behind a diverging lens with a focal length of 86 cm. What is the height of the image?
    a) 2.77 x 10$^{-1}$ cm
    b) 3.32 x 10$^{-1}$ cm
    c) 3.99 x 10$^{-1}$ cm
    d) 4.78 x 10$^{-1}$ cm
    e) 5.74 x 10$^{-1}$ cm
12) An object is placed 3.15 cm to the left of a converging lens with a focal length of 6.7 cm. How far is the image from the lens?
    a) 3.34 x 10$^0$ cm
    b) 5.95 x 10$^0$ cm
    c) 1.06 x 10$^1$ cm
    d) 1.88 x 10$^1$ cm
    e) 3.34 x 10$^1$ cm

### KEY:PhysicsCalc2:T3:V0

PhysicsCalc2152657831440
1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:
    -a) 9$^2$ + (2-s)$^2$
    -b) 9$^2$ + (7-s)$^2$
    -c) 7$^2$ + (2-s)$^2$
    +d) 2$^2$ + (9-s)$^2$
    -e) 2$^2$ + (7-s)$^2$
2) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?
    -a) 11.67 Joules
    -b) 2.5 Watts
    +c) 1.67 Watts
    -d) None of these are ture.
3) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e$^3$? (where e =2.7...)
    +a) 1.88 x 10$^9$ s.
    -b) 5.93 x 10$^9$ s.
    -c) 1.88 x 10$^{10}$ s.
    -d) 5.93 x 10$^{10}$ s.
    -e) 1.88 x 10$^{11}$ s.
4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
    -a) 5.14 x 10$^{-5}$ Volts
    +b) 1.62 x 10$^{-4}$ Volts
    -c) 5.14 x 10$^{-4}$ Volts
    -d) 1.62 x 10$^{-3}$ Volts
    -e) 5.14 x 10$^{-3}$ Volts
5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?
    -a) 1.1 x 10$^0$ volts
    -b) 3.6 x 10$^0$ volts
    -c) 1.1 x 10$^1$ volts
    +d) 3.6 x 10$^1$ volts
    -e) 1.1 x 10$^2$ volts
6) An loop of wire with 54 turns has a radius of 0.8 meters, and is oriented with its axis parallel to a magetic field of 0.86 Tesla. What is the induced voltage if this field is reduced to 46% of its original value in 2.4 seconds?
    -a) 1.43 x 10$^1$ volts
    -b) 1.73 x 10$^1$ volts
    +c) 2.1 x 10$^1$ volts
    -d) 2.55 x 10$^1$ volts
    -e) 3.08 x 10$^1$ volts
7) An important principle that allows fiber optics to work is
    -a) the invariance of the speed of light
    +b) total internal reflection
    -c) the Doppler shift
    -d) partial internal absorption
    -e) total external refraction
8) The focal point is where
    +a) rays meet if they were parallel to the optical axis before striking a lens
    -b) rays meet whenever they are forming an image
    -c) rays meet whenever they pass through a lens
    -d) the center of the lens
    -e) rays meet if they are parallel to each other
9) The law of reflection applies to
    +a) both flat and curved surfaces
    -b) flat surfaces
    -c) curved surfaces
    -d) telescopes but not microscopes
    -e) only light in a vacuum
10) In optics, normal means
    -a) to the right of the optical axis
    -b) to the left of the optical axis
    +c) perpendicular to the surface
    -d) parallel to the surface
11) An object of height 0.75 cm is placed 147 cm behind a diverging lens with a focal length of 86 cm. What is the height of the image?
    +a) 2.77 x 10$^{-1}$ cm
    -b) 3.32 x 10$^{-1}$ cm
    -c) 3.99 x 10$^{-1}$ cm
    -d) 4.78 x 10$^{-1}$ cm
    -e) 5.74 x 10$^{-1}$ cm
12) An object is placed 3.15 cm to the left of a converging lens with a focal length of 6.7 cm. How far is the image from the lens?
    -a) 3.34 x 10$^0$ cm
    +b) 5.95 x 10$^0$ cm
    -c) 1.06 x 10$^1$ cm
    -d) 1.88 x 10$^1$ cm
    -e) 3.34 x 10$^1$ cm

### PhysicsCalc2:T3:V1

PhysicsCalc2152657831440
1) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?
    a) 1.1 x 10$^0$ volts
    b) 3.6 x 10$^0$ volts
    c) 1.1 x 10$^1$ volts
    d) 3.6 x 10$^1$ volts
    e) 1.1 x 10$^2$ volts
2) An object is placed 4.85 cm to the left of a converging lens with a focal length of 4 cm. How far is the image from the lens?
    a) 4.06 x 10$^0$ cm
    b) 7.22 x 10$^0$ cm
    c) 1.28 x 10$^1$ cm
    d) 2.28 x 10$^1$ cm
    e) 4.06 x 10$^1$ cm
3) An important principle that allows fiber optics to work is
    a) the Doppler shift
    b) partial internal absorption
    c) the invariance of the speed of light
    d) total external refraction
    e) total internal reflection
4) The law of reflection applies to
    a) curved surfaces
    b) flat surfaces
    c) telescopes but not microscopes
    d) only light in a vacuum
    e) both flat and curved surfaces
5) The focal point is where
    a) rays meet if they are parallel to each other
    b) rays meet whenever they pass through a lens
    c) rays meet whenever they are forming an image
    d) rays meet if they were parallel to the optical axis before striking a lens
    e) the center of the lens
6) An object of height 0.64 cm is placed 112 cm behind a diverging lens with a focal length of 65 cm. What is the height of the image?
    a) 1.36 x 10$^{-1}$ cm
    b) 1.63 x 10$^{-1}$ cm
    c) 1.96 x 10$^{-1}$ cm
    d) 2.35 x 10$^{-1}$ cm
    e) 2.82 x 10$^{-1}$ cm
7) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e$^3$? (where e =2.7...)
    a) 1.88 x 10$^9$ s.
    b) 5.93 x 10$^9$ s.
    c) 1.88 x 10$^{10}$ s.
    d) 5.93 x 10$^{10}$ s.
    e) 1.88 x 10$^{11}$ s.
8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:
    a) 2$^2$ + (7-s)$^2$
    b) 7$^2$ + (2-s)$^2$
    c) 9$^2$ + (2-s)$^2$
    d) 9$^2$ + (7-s)$^2$
    e) 2$^2$ + (9-s)$^2$
9) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?
    a) 1.67 Watts
    b) 11.67 Joules
    c) None of these are ture.
    d) 2.5 Watts
10) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?
    a) 5.43 x 10$^0$ volts
    b) 6.58 x 10$^0$ volts
    c) 7.97 x 10$^0$ volts
    d) 9.65 x 10$^0$ volts
    e) 1.17 x 10$^1$ volts
11) In optics, normal means
    a) to the right of the optical axis
    b) parallel to the surface
    c) perpendicular to the surface
    d) to the left of the optical axis
12) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
    a) 5.14 x 10$^{-5}$ Volts
    b) 1.62 x 10$^{-4}$ Volts
    c) 5.14 x 10$^{-4}$ Volts
    d) 1.62 x 10$^{-3}$ Volts
    e) 5.14 x 10$^{-3}$ Volts

### KEY:PhysicsCalc2:T3:V1

PhysicsCalc2152657831440
1) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?
    -a) 1.1 x 10$^0$ volts
    -b) 3.6 x 10$^0$ volts
    -c) 1.1 x 10$^1$ volts
    +d) 3.6 x 10$^1$ volts
    -e) 1.1 x 10$^2$ volts
2) An object is placed 4.85 cm to the left of a converging lens with a focal length of 4 cm. How far is the image from the lens?
    -a) 4.06 x 10$^0$ cm
    -b) 7.22 x 10$^0$ cm
    -c) 1.28 x 10$^1$ cm
    +d) 2.28 x 10$^1$ cm
    -e) 4.06 x 10$^1$ cm
3) An important principle that allows fiber optics to work is
    -a) the Doppler shift
    -b) partial internal absorption
    -c) the invariance of the speed of light
    -d) total external refraction
    +e) total internal reflection
4) The law of reflection applies to
    -a) curved surfaces
    -b) flat surfaces
    -c) telescopes but not microscopes
    -d) only light in a vacuum
    +e) both flat and curved surfaces
5) The focal point is where
    -a) rays meet if they are parallel to each other
    -b) rays meet whenever they pass through a lens
    -c) rays meet whenever they are forming an image
    +d) rays meet if they were parallel to the optical axis before striking a lens
    -e) the center of the lens
6) An object of height 0.64 cm is placed 112 cm behind a diverging lens with a focal length of 65 cm. What is the height of the image?
    -a) 1.36 x 10$^{-1}$ cm
    -b) 1.63 x 10$^{-1}$ cm
    -c) 1.96 x 10$^{-1}$ cm
    +d) 2.35 x 10$^{-1}$ cm
    -e) 2.82 x 10$^{-1}$ cm
7) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e$^3$? (where e =2.7...)
    +a) 1.88 x 10$^9$ s.
    -b) 5.93 x 10$^9$ s.
    -c) 1.88 x 10$^{10}$ s.
    -d) 5.93 x 10$^{10}$ s.
    -e) 1.88 x 10$^{11}$ s.
8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:
    -a) 2$^2$ + (7-s)$^2$
    -b) 7$^2$ + (2-s)$^2$
    -c) 9$^2$ + (2-s)$^2$
    -d) 9$^2$ + (7-s)$^2$
    +e) 2$^2$ + (9-s)$^2$
9) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?
    +a) 1.67 Watts
    -b) 11.67 Joules
    -c) None of these are ture.
    -d) 2.5 Watts
10) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?
    -a) 5.43 x 10$^0$ volts
    +b) 6.58 x 10$^0$ volts
    -c) 7.97 x 10$^0$ volts
    -d) 9.65 x 10$^0$ volts
    -e) 1.17 x 10$^1$ volts
11) In optics, normal means
    -a) to the right of the optical axis
    -b) parallel to the surface
    +c) perpendicular to the surface
    -d) to the left of the optical axis
12) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
    -a) 5.14 x 10$^{-5}$ Volts
    +b) 1.62 x 10$^{-4}$ Volts
    -c) 5.14 x 10$^{-4}$ Volts
    -d) 1.62 x 10$^{-3}$ Volts
    -e) 5.14 x 10$^{-3}$ Volts

### PhysicsCalc2:T3:V2

PhysicsCalc2152657831440
1) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e$^3$? (where e =2.7...)
    a) 1.88 x 10$^9$ s.
    b) 5.93 x 10$^9$ s.
    c) 1.88 x 10$^{10}$ s.
    d) 5.93 x 10$^{10}$ s.
    e) 1.88 x 10$^{11}$ s.
2) An object of height 0.75 cm is placed 147 cm behind a diverging lens with a focal length of 86 cm. What is the height of the image?
    a) 2.77 x 10$^{-1}$ cm
    b) 3.32 x 10$^{-1}$ cm
    c) 3.99 x 10$^{-1}$ cm
    d) 4.78 x 10$^{-1}$ cm
    e) 5.74 x 10$^{-1}$ cm
3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:
    a) 9$^2$ + (2-s)$^2$
    b) 2$^2$ + (9-s)$^2$
    c) 2$^2$ + (7-s)$^2$
    d) 7$^2$ + (2-s)$^2$
    e) 9$^2$ + (7-s)$^2$
4) An object is placed 4.35 cm to the left of a converging lens with a focal length of 5.7 cm. How far is the image from the lens?
    a) 1.03 x 10$^1$ cm
    b) 1.84 x 10$^1$ cm
    c) 3.27 x 10$^1$ cm
    d) 5.81 x 10$^1$ cm
    e) 1.03 x 10$^2$ cm
5) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?
    a) 11.67 Joules
    b) 1.67 Watts
    c) None of these are ture.
    d) 2.5 Watts
6) An important principle that allows fiber optics to work is
    a) total internal reflection
    b) partial internal absorption
    c) the invariance of the speed of light
    d) the Doppler shift
    e) total external refraction
7) The law of reflection applies to
    a) telescopes but not microscopes
    b) both flat and curved surfaces
    c) flat surfaces
    d) curved surfaces
    e) only light in a vacuum
8) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?
    a) 1.1 x 10$^0$ volts
    b) 3.6 x 10$^0$ volts
    c) 1.1 x 10$^1$ volts
    d) 3.6 x 10$^1$ volts
    e) 1.1 x 10$^2$ volts
9) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?
    a) 1.06 x 10$^0$ volts
    b) 1.29 x 10$^0$ volts
    c) 1.56 x 10$^0$ volts
    d) 1.89 x 10$^0$ volts
    e) 2.29 x 10$^0$ volts
10) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
    a) 5.14 x 10$^{-5}$ Volts
    b) 1.62 x 10$^{-4}$ Volts
    c) 5.14 x 10$^{-4}$ Volts
    d) 1.62 x 10$^{-3}$ Volts
    e) 5.14 x 10$^{-3}$ Volts
11) In optics, normal means
    a) parallel to the surface
    b) to the left of the optical axis
    c) perpendicular to the surface
    d) to the right of the optical axis
12) The focal point is where
    a) rays meet whenever they pass through a lens
    b) rays meet if they are parallel to each other
    c) the center of the lens
    d) rays meet if they were parallel to the optical axis before striking a lens
    e) rays meet whenever they are forming an image

### KEY:PhysicsCalc2:T3:V2

PhysicsCalc2152657831440
1) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e$^3$? (where e =2.7...)
    +a) 1.88 x 10$^9$ s.
    -b) 5.93 x 10$^9$ s.
    -c) 1.88 x 10$^{10}$ s.
    -d) 5.93 x 10$^{10}$ s.
    -e) 1.88 x 10$^{11}$ s.
2) An object of height 0.75 cm is placed 147 cm behind a diverging lens with a focal length of 86 cm. What is the height of the image?
    +a) 2.77 x 10$^{-1}$ cm
    -b) 3.32 x 10$^{-1}$ cm
    -c) 3.99 x 10$^{-1}$ cm
    -d) 4.78 x 10$^{-1}$ cm
    -e) 5.74 x 10$^{-1}$ cm
3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:
    -a) 9$^2$ + (2-s)$^2$
    +b) 2$^2$ + (9-s)$^2$
    -c) 2$^2$ + (7-s)$^2$
    -d) 7$^2$ + (2-s)$^2$
    -e) 9$^2$ + (7-s)$^2$
4) An object is placed 4.35 cm to the left of a converging lens with a focal length of 5.7 cm. How far is the image from the lens?
    -a) 1.03 x 10$^1$ cm
    +b) 1.84 x 10$^1$ cm
    -c) 3.27 x 10$^1$ cm
    -d) 5.81 x 10$^1$ cm
    -e) 1.03 x 10$^2$ cm
5) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?
    -a) 11.67 Joules
    +b) 1.67 Watts
    -c) None of these are ture.
    -d) 2.5 Watts
6) An important principle that allows fiber optics to work is
    +a) total internal reflection
    -b) partial internal absorption
    -c) the invariance of the speed of light
    -d) the Doppler shift
    -e) total external refraction
7) The law of reflection applies to
    -a) telescopes but not microscopes
    +b) both flat and curved surfaces
    -c) flat surfaces
    -d) curved surfaces
    -e) only light in a vacuum
8) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?
    -a) 1.1 x 10$^0$ volts
    -b) 3.6 x 10$^0$ volts
    -c) 1.1 x 10$^1$ volts
    +d) 3.6 x 10$^1$ volts
    -e) 1.1 x 10$^2$ volts
9) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?
    -a) 1.06 x 10$^0$ volts
    -b) 1.29 x 10$^0$ volts
    -c) 1.56 x 10$^0$ volts
    -d) 1.89 x 10$^0$ volts
    +e) 2.29 x 10$^0$ volts
10) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
    -a) 5.14 x 10$^{-5}$ Volts
    +b) 1.62 x 10$^{-4}$ Volts
    -c) 5.14 x 10$^{-4}$ Volts
    -d) 1.62 x 10$^{-3}$ Volts
    -e) 5.14 x 10$^{-3}$ Volts
11) In optics, normal means
    -a) parallel to the surface
    -b) to the left of the optical axis
    +c) perpendicular to the surface
    -d) to the right of the optical axis
12) The focal point is where
    -a) rays meet whenever they pass through a lens
    -b) rays meet if they are parallel to each other
    -c) the center of the lens
    +d) rays meet if they were parallel to the optical axis before striking a lens
    -e) rays meet whenever they are forming an image

### PhysicsCalc2:T4:V0

PhysicsCalc2152657831440
1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a$^2$, where β equals
    a) 1.61 x 10$^{-3}$ unit
    b) 1.95 x 10$^{-3}$ unit
    c) 2.36 x 10$^{-3}$ unit
    d) 2.86 x 10$^{-3}$ unit
    e) 3.46 x 10$^{-3}$ unit
2) An object is placed 4.35 cm to the left of a converging lens with a focal length of 5.7 cm. How far is the image from the lens?
    a) 1.03 x 10$^1$ cm
    b) 1.84 x 10$^1$ cm
    c) 3.27 x 10$^1$ cm
    d) 5.81 x 10$^1$ cm
    e) 1.03 x 10$^2$ cm
3) Which lens has the shorter focal length?
    a) They have the same focal lengh.
    b)
    c)
4) If this represents the eye looking at an object, where is this object?
    a) Two (of the other answers) are true
    b) directly in front of the eye (almost touching)
    c) One focal length in front of the eye
    d) at infinity
    e) very far away
5) Amphere's law for magnetostatic currents is that $\oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}$ equals the current enclosed by the closed loop, and $B=\mu _{0}H$ is the magnetic field. A current of 5.8A flows upward along the z axis. Noting that for this geometry, $\oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell$, calculate the line integral $\oint d\ell$ for a circle of radius 4.4m.
    a) 2.30E+01 m
    b) 2.52E+01 m
    c) 2.76E+01 m
    d) 3.03E+01 m
    e) 3.32E+01 m
6) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H$ at a distance of 6.2m from a wire carrying a current of 4.8A?
    a) 9.35E-02 A/m
    b) 1.02E-01 A/m
    c) 1.12E-01 A/m
    d) 1.23E-01 A/m
    e) 1.35E-01 A/m
    a) 5.31E+01 amps per meter
    b) 5.73E+01 amps per meter
    c) 6.19E+01 amps per meter
    d) 6.68E+01 amps per meter
    e) 7.21E+01 amps per meter
8) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H_{y}$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?
    a) 1.28E-01 A/m
    b) 1.40E-01 A/m
    c) 1.54E-01 A/m
    d) 1.68E-01 A/m
    e) 1.85E-01 A/m
9) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 96A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (-6.4, 6.4) to the point (6.4, 6.4).
    a) 2.00E+01 amps
    b) 2.19E+01 amps
    c) 2.40E+01 amps
    d) 2.63E+01 amps
    e) 2.89E+01 amps
10) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,8.6) to the point (8.6,8.6).
    a) 4.50E+00 amps
    b) 4.93E+00 amps
    c) 5.41E+00 amps
    d) 5.93E+00 amps
    e) 6.50E+00 amps
11) A circlular capactitor of radius 4.8 m has a gap of 9 mm, and a charge of 53 μC. The capacitor is discharged through a 6 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
    a) 3.26E-09 Tesla
    b) 4.11E-09 Tesla
    c) 5.17E-09 Tesla
    d) 6.51E-09 Tesla
    e) 8.19E-09 Tesla
12) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?
    a) 3.07E-04 s
    b) 3.71E-04 s
    c) 4.50E-04 s
    d) 5.45E-04 s
    e) 6.61E-04 s

### KEY:PhysicsCalc2:T4:V0

PhysicsCalc2152657831440
1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a$^2$, where β equals
    +a) 1.61 x 10$^{-3}$ unit
    -b) 1.95 x 10$^{-3}$ unit
    -c) 2.36 x 10$^{-3}$ unit
    -d) 2.86 x 10$^{-3}$ unit
    -e) 3.46 x 10$^{-3}$ unit
2) An object is placed 4.35 cm to the left of a converging lens with a focal length of 5.7 cm. How far is the image from the lens?
    -a) 1.03 x 10$^1$ cm
    +b) 1.84 x 10$^1$ cm
    -c) 3.27 x 10$^1$ cm
    -d) 5.81 x 10$^1$ cm
    -e) 1.03 x 10$^2$ cm
3) Which lens has the shorter focal length?
    -a) They have the same focal lengh.
    -b)
    +c)
4) If this represents the eye looking at an object, where is this object?
    +a) Two (of the other answers) are true
    -b) directly in front of the eye (almost touching)
    -c) One focal length in front of the eye
    -d) at infinity
    -e) very far away
5) Amphere's law for magnetostatic currents is that $\oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}$ equals the current enclosed by the closed loop, and $B=\mu _{0}H$ is the magnetic field. A current of 5.8A flows upward along the z axis. Noting that for this geometry, $\oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell$, calculate the line integral $\oint d\ell$ for a circle of radius 4.4m.
    -a) 2.30E+01 m
    -b) 2.52E+01 m
    +c) 2.76E+01 m
    -d) 3.03E+01 m
    -e) 3.32E+01 m
6) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H$ at a distance of 6.2m from a wire carrying a current of 4.8A?
    -a) 9.35E-02 A/m
    -b) 1.02E-01 A/m
    -c) 1.12E-01 A/m
    +d) 1.23E-01 A/m
    -e) 1.35E-01 A/m
    -a) 5.31E+01 amps per meter
    -b) 5.73E+01 amps per meter
    -c) 6.19E+01 amps per meter
    -d) 6.68E+01 amps per meter
    +e) 7.21E+01 amps per meter
8) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H_{y}$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?
    -a) 1.28E-01 A/m
    -b) 1.40E-01 A/m
    -c) 1.54E-01 A/m
    +d) 1.68E-01 A/m
    -e) 1.85E-01 A/m
9) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 96A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (-6.4, 6.4) to the point (6.4, 6.4).
    -a) 2.00E+01 amps
    -b) 2.19E+01 amps
    +c) 2.40E+01 amps
    -d) 2.63E+01 amps
    -e) 2.89E+01 amps
10) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,8.6) to the point (8.6,8.6).
    +a) 4.50E+00 amps
    -b) 4.93E+00 amps
    -c) 5.41E+00 amps
    -d) 5.93E+00 amps
    -e) 6.50E+00 amps
11) A circlular capactitor of radius 4.8 m has a gap of 9 mm, and a charge of 53 μC. The capacitor is discharged through a 6 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
    -a) 3.26E-09 Tesla
    -b) 4.11E-09 Tesla
    +c) 5.17E-09 Tesla
    -d) 6.51E-09 Tesla
    -e) 8.19E-09 Tesla
12) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?
    -a) 3.07E-04 s
    -b) 3.71E-04 s
    +c) 4.50E-04 s
    -d) 5.45E-04 s
    -e) 6.61E-04 s

### PhysicsCalc2:T4:V1

PhysicsCalc2152657831440
1) If this represents the eye looking at an object, where is this object?
    a) One focal length in front of the eye
    b) directly in front of the eye (almost touching)
    c) very far away
    d) Two (of the other answers) are true
    e) at infinity
2) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H$ at a distance of 8.2m from a wire carrying a current of 7.2A?
    a) 9.67E-02 A/m
    b) 1.06E-01 A/m
    c) 1.16E-01 A/m
    d) 1.27E-01 A/m
    e) 1.40E-01 A/m
3) Which lens has the shorter focal length?
    a)
    b)
    c) They have the same focal lengh.
4) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (-6.1, 6.1) to the point (6.1, 6.1).
    a) 1.50E+01 amps
    b) 1.65E+01 amps
    c) 1.81E+01 amps
    d) 1.98E+01 amps
    e) 2.18E+01 amps
5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a$^2$, where β equals
    a) 3.38 x 10$^{-3}$ unit
    b) 4.1 x 10$^{-3}$ unit
    c) 4.96 x 10$^{-3}$ unit
    d) 6.01 x 10$^{-3}$ unit
    e) 7.28 x 10$^{-3}$ unit
6) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,5) to the point (5,5).
    a) 7.44E+00 amps
    b) 8.15E+00 amps
    c) 8.94E+00 amps
    d) 9.80E+00 amps
    e) 1.08E+01 amps
7) What is the sum of 7.2 apples plus 9 apples?
    a) 1.62E+01 apples
    b) 1.78E+01 apples
    c) 1.95E+01 apples
    d) 2.14E+01 apples
    e) 2.34E+01 apples
8) A circlular capactitor of radius 4.6 m has a gap of 15 mm, and a charge of 57 μC. The capacitor is discharged through a 9 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
    a) 4.43E-09 Tesla
    b) 5.57E-09 Tesla
    c) 7.02E-09 Tesla
    d) 8.83E-09 Tesla
    e) 1.11E-08 Tesla
9) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H_{y}$ at the point (6.3551,4.3477) if a current of 4.8A flows through a wire that runs along the z axis?
    a) 8.19E-02 A/m
    b) 8.98E-02 A/m
    c) 9.84E-02 A/m
    d) 1.08E-01 A/m
    e) 1.18E-01 A/m
10) An object is placed 6.55 cm to the left of a converging lens with a focal length of 5.4 cm. How far is the image from the lens?
    a) 3.08 x 10$^0$ cm
    b) 5.47 x 10$^0$ cm
    c) 9.73 x 10$^0$ cm
    d) 1.73 x 10$^1$ cm
    e) 3.08 x 10$^1$ cm
11) A circlular capactitor of radius 3.7 m has a gap of 15 mm, and a charge of 36 μC. The capacitor is discharged through a 6 kΩ resistor. What is the decay time?
    a) 1.04E-04 s
    b) 1.26E-04 s
    c) 1.52E-04 s
    d) 1.85E-04 s
    e) 2.24E-04 s
12) Amphere's law for magnetostatic currents is that $\oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}$ equals the current enclosed by the closed loop, and $B=\mu _{0}H$ is the magnetic field. A current of 9.8A flows upward along the z axis. Noting that for this geometry, $\oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell$, calculate the line integral $\oint d\ell$ for a circle of radius 4.6m.
    a) 2.89E+01 m
    b) 3.17E+01 m
    c) 3.47E+01 m
    d) 3.81E+01 m
    e) 4.18E+01 m

### KEY:PhysicsCalc2:T4:V1

PhysicsCalc2152657831440
1) If this represents the eye looking at an object, where is this object?
    -a) One focal length in front of the eye
    -b) directly in front of the eye (almost touching)
    -c) very far away
    +d) Two (of the other answers) are true
    -e) at infinity
2) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H$ at a distance of 8.2m from a wire carrying a current of 7.2A?
    -a) 9.67E-02 A/m
    -b) 1.06E-01 A/m
    -c) 1.16E-01 A/m
    -d) 1.27E-01 A/m
    +e) 1.40E-01 A/m
3) Which lens has the shorter focal length?
    -a)
    +b)
    -c) They have the same focal lengh.
4) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (-6.1, 6.1) to the point (6.1, 6.1).
    -a) 1.50E+01 amps
    -b) 1.65E+01 amps
    -c) 1.81E+01 amps
    -d) 1.98E+01 amps
    +e) 2.18E+01 amps
5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a$^2$, where β equals
    -a) 3.38 x 10$^{-3}$ unit
    -b) 4.1 x 10$^{-3}$ unit
    -c) 4.96 x 10$^{-3}$ unit
    -d) 6.01 x 10$^{-3}$ unit
    +e) 7.28 x 10$^{-3}$ unit
6) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,5) to the point (5,5).
    -a) 7.44E+00 amps
    -b) 8.15E+00 amps
    -c) 8.94E+00 amps
    -d) 9.80E+00 amps
    +e) 1.08E+01 amps
7) What is the sum of 7.2 apples plus 9 apples?
    +a) 1.62E+01 apples
    -b) 1.78E+01 apples
    -c) 1.95E+01 apples
    -d) 2.14E+01 apples
    -e) 2.34E+01 apples
8) A circlular capactitor of radius 4.6 m has a gap of 15 mm, and a charge of 57 μC. The capacitor is discharged through a 9 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
    -a) 4.43E-09 Tesla
    -b) 5.57E-09 Tesla
    +c) 7.02E-09 Tesla
    -d) 8.83E-09 Tesla
    -e) 1.11E-08 Tesla
9) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H_{y}$ at the point (6.3551,4.3477) if a current of 4.8A flows through a wire that runs along the z axis?
    +a) 8.19E-02 A/m
    -b) 8.98E-02 A/m
    -c) 9.84E-02 A/m
    -d) 1.08E-01 A/m
    -e) 1.18E-01 A/m
10) An object is placed 6.55 cm to the left of a converging lens with a focal length of 5.4 cm. How far is the image from the lens?
    -a) 3.08 x 10$^0$ cm
    -b) 5.47 x 10$^0$ cm
    -c) 9.73 x 10$^0$ cm
    -d) 1.73 x 10$^1$ cm
    +e) 3.08 x 10$^1$ cm
11) A circlular capactitor of radius 3.7 m has a gap of 15 mm, and a charge of 36 μC. The capacitor is discharged through a 6 kΩ resistor. What is the decay time?
    -a) 1.04E-04 s
    -b) 1.26E-04 s
    +c) 1.52E-04 s
    -d) 1.85E-04 s
    -e) 2.24E-04 s
12) Amphere's law for magnetostatic currents is that $\oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}$ equals the current enclosed by the closed loop, and $B=\mu _{0}H$ is the magnetic field. A current of 9.8A flows upward along the z axis. Noting that for this geometry, $\oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell$, calculate the line integral $\oint d\ell$ for a circle of radius 4.6m.
    +a) 2.89E+01 m
    -b) 3.17E+01 m
    -c) 3.47E+01 m
    -d) 3.81E+01 m
    -e) 4.18E+01 m

### PhysicsCalc2:T4:V2

PhysicsCalc2152657831440
1) If this represents the eye looking at an object, where is this object?
    a) Two (of the other answers) are true
    b) One focal length in front of the eye
    c) directly in front of the eye (almost touching)
    d) very far away
    e) at infinity
2) An object is placed 3.15 cm to the left of a converging lens with a focal length of 6.7 cm. How far is the image from the lens?
    a) 3.34 x 10$^0$ cm
    b) 5.95 x 10$^0$ cm
    c) 1.06 x 10$^1$ cm
    d) 1.88 x 10$^1$ cm
    e) 3.34 x 10$^1$ cm
3) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (-7.4, 7.4) to the point (7.4, 7.4).
    a) 1.69E+01 amps
    b) 1.85E+01 amps
    c) 2.03E+01 amps
    d) 2.22E+01 amps
    e) 2.44E+01 amps
4) Which lens has the shorter focal length?
    a) They have the same focal lengh.
    b)
    c)
5) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 49A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,9.8) to the point (9.8,9.8).
    a) 6.13E+00 amps
    b) 6.72E+00 amps
    c) 7.36E+00 amps
    d) 8.07E+00 amps
    e) 8.85E+00 amps
6) A circlular capactitor of radius 4.8 m has a gap of 9 mm, and a charge of 53 μC. The capacitor is discharged through a 6 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
    a) 3.26E-09 Tesla
    b) 4.11E-09 Tesla
    c) 5.17E-09 Tesla
    d) 6.51E-09 Tesla
    e) 8.19E-09 Tesla
7) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H$ at a distance of 6.8m from a wire carrying a current of 6.5A?
    a) 1.39E-01 A/m
    b) 1.52E-01 A/m
    c) 1.67E-01 A/m
    d) 1.83E-01 A/m
    e) 2.01E-01 A/m
8) What is the sum of 6.6 apples plus 33 apples?
    a) 3.61E+01 apples
    b) 3.96E+01 apples
    c) 4.34E+01 apples
    d) 4.76E+01 apples
    e) 5.22E+01 apples
9) Amphere's law for magnetostatic currents is that $\oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}$ equals the current enclosed by the closed loop, and $B=\mu _{0}H$ is the magnetic field. A current of 7.3A flows upward along the z axis. Noting that for this geometry, $\oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell$, calculate the line integral $\oint d\ell$ for a circle of radius 8.3m.
    a) 4.76E+01 m
    b) 5.22E+01 m
    c) 5.72E+01 m
    d) 6.27E+01 m
    e) 6.87E+01 m
10) A circlular capactitor of radius 4 m has a gap of 14 mm, and a charge of 24 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?
    a) 1.84E-04 s
    b) 2.23E-04 s
    c) 2.70E-04 s
    d) 3.27E-04 s
    e) 3.96E-04 s
11) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a$^2$, where β equals
    a) 1.33 x 10$^{-3}$ unit
    b) 1.61 x 10$^{-3}$ unit
    c) 1.95 x 10$^{-3}$ unit
    d) 2.36 x 10$^{-3}$ unit
    e) 2.86 x 10$^{-3}$ unit
12) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H_{y}$ at the point (7.9293,2.4528) if a current of 7.3A flows through a wire that runs along the z axis?
    a) 1.11E-01 A/m
    b) 1.22E-01 A/m
    c) 1.34E-01 A/m
    d) 1.47E-01 A/m
    e) 1.61E-01 A/m

### KEY:PhysicsCalc2:T4:V2

PhysicsCalc2152657831440
1) If this represents the eye looking at an object, where is this object?
    +a) Two (of the other answers) are true
    -b) One focal length in front of the eye
    -c) directly in front of the eye (almost touching)
    -d) very far away
    -e) at infinity
2) An object is placed 3.15 cm to the left of a converging lens with a focal length of 6.7 cm. How far is the image from the lens?
    -a) 3.34 x 10$^0$ cm
    +b) 5.95 x 10$^0$ cm
    -c) 1.06 x 10$^1$ cm
    -d) 1.88 x 10$^1$ cm
    -e) 3.34 x 10$^1$ cm
3) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (-7.4, 7.4) to the point (7.4, 7.4).
    -a) 1.69E+01 amps
    +b) 1.85E+01 amps
    -c) 2.03E+01 amps
    -d) 2.22E+01 amps
    -e) 2.44E+01 amps
4) Which lens has the shorter focal length?
    -a) They have the same focal lengh.
    +b)
    -c)
5) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 49A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,9.8) to the point (9.8,9.8).
    +a) 6.13E+00 amps
    -b) 6.72E+00 amps
    -c) 7.36E+00 amps
    -d) 8.07E+00 amps
    -e) 8.85E+00 amps
6) A circlular capactitor of radius 4.8 m has a gap of 9 mm, and a charge of 53 μC. The capacitor is discharged through a 6 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
    -a) 3.26E-09 Tesla
    -b) 4.11E-09 Tesla
    +c) 5.17E-09 Tesla
    -d) 6.51E-09 Tesla
    -e) 8.19E-09 Tesla
7) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H$ at a distance of 6.8m from a wire carrying a current of 6.5A?
    -a) 1.39E-01 A/m
    +b) 1.52E-01 A/m
    -c) 1.67E-01 A/m
    -d) 1.83E-01 A/m
    -e) 2.01E-01 A/m
8) What is the sum of 6.6 apples plus 33 apples?
    -a) 3.61E+01 apples
    +b) 3.96E+01 apples
    -c) 4.34E+01 apples
    -d) 4.76E+01 apples
    -e) 5.22E+01 apples
9) Amphere's law for magnetostatic currents is that $\oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}$ equals the current enclosed by the closed loop, and $B=\mu _{0}H$ is the magnetic field. A current of 7.3A flows upward along the z axis. Noting that for this geometry, $\oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell$, calculate the line integral $\oint d\ell$ for a circle of radius 8.3m.
    -a) 4.76E+01 m
    +b) 5.22E+01 m
    -c) 5.72E+01 m
    -d) 6.27E+01 m
    -e) 6.87E+01 m
10) A circlular capactitor of radius 4 m has a gap of 14 mm, and a charge of 24 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?
    -a) 1.84E-04 s
    +b) 2.23E-04 s
    -c) 2.70E-04 s
    -d) 3.27E-04 s
    -e) 3.96E-04 s
11) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a$^2$, where β equals
    -a) 1.33 x 10$^{-3}$ unit
    +b) 1.61 x 10$^{-3}$ unit
    -c) 1.95 x 10$^{-3}$ unit
    -d) 2.36 x 10$^{-3}$ unit
    -e) 2.86 x 10$^{-3}$ unit
12) If $H=B/\mu _{0}$, where $B$ is magnetic field, what is $H_{y}$ at the point (7.9293,2.4528) if a current of 7.3A flows through a wire that runs along the z axis?
    -a) 1.11E-01 A/m
    -b) 1.22E-01 A/m
    +c) 1.34E-01 A/m
    -d) 1.47E-01 A/m
    -e) 1.61E-01 A/m

### PhysicsCalc2:FE:V0

PhysicsCalc2152657831440
1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a$^2$, where β equals
    a) 1.52 x 10$^{-4}$ unit
    b) 1.85 x 10$^{-4}$ unit
    c) 2.24 x 10$^{-4}$ unit
    d) 2.71 x 10$^{-4}$ unit
    e) 3.28 x 10$^{-4}$ unit
2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$
    a) 3
    b) 1/2
    c) 2
    d) 3/2
3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    a) $2R\varepsilon _{0}E=r^{2}\rho$
    b) $2\varepsilon _{0}E=r\rho$
    c) none of these are correct
    d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    e) $2r\varepsilon _{0}E=R^{2}\rho$
4) A parallel plate capacitor has both plates with an area of 1.35 m$^2$. The separation between the plates is 1.23mm. Applied to the plates is a potential difference of 2.65 kV. What is the capacitance?
    a) 7.35 nF.
    b) 8.45 nF.
    c) 9.72 nF.
    d) 11.18 nF.
    e) 12.85 nF.
5) What voltage is required accelerate an electron at rest to a speed of 7.6 x 10$^7$ m/s?
    a) 3.2 x 10$^3$ volts
    b) 4.9 x 10$^3$ volts
    c) 7.3 x 10$^3$ volts
    d) 1.1 x 10$^4$ volts
    e) 1.6 x 10$^4$ volts
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(1.89+1.31z)\rho ^{3}{\hat {\rho }}+8.35z^{2}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    a) 5.311E+02
    b) 6.434E+02
    c) 7.795E+02
    d) 9.444E+02
    e) 1.144E+03
7) The diameter of a copper wire is 9.9 mm, and it carries a current of 41 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    a) 2.24 x 10$^{-5}$m/s
    b) 2.72 x 10$^{-5}$m/s
    c) 3.29 x 10$^{-5}$m/s
    d) 3.99 x 10$^{-5}$m/s
    e) 4.83 x 10$^{-5}$m/s
8) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?
    a) ${\frac {6}{11}}\Omega$.
    b) ${\frac {6}{3}}\Omega$.
    c) ${\frac {11}{6}}\Omega$.
    d) ${\frac {3}{6}}\Omega$.
9) A 5.8 ohm resistor is connected in series to a pair of 2.8 ohm resistors that are in parallel. What is the net resistance?
    a) 7.2 ohms.
    b) 8.3 ohms.
    c) 9.5 ohms.
    d) 11 ohms.
    e) 12.6 ohms.
10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?
    a) 1.3 x 10$^2$ m.
    b) 4.1 x 10$^2$ m.
    c) 1.3 x 10$^3$ m.
    d) 4.1 x 10$^3$ m.
    e) 1.3 x 10$^4$ m.
11) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?
    a) 5.43 x 10$^0$ volts
    b) 6.58 x 10$^0$ volts
    c) 7.97 x 10$^0$ volts
    d) 9.65 x 10$^0$ volts
    e) 1.17 x 10$^1$ volts
12) An object is placed 3.55 cm to the left of a converging lens with a focal length of 6.8 cm. How far is the image from the lens?
    a) 4.18 x 10$^0$ cm
    b) 7.43 x 10$^0$ cm
    c) 1.32 x 10$^1$ cm
    d) 2.35 x 10$^1$ cm
    e) 4.18 x 10$^1$ cm
13) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$\int {\vec {H}}\cdot {\vec {d\ell }}$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?
    a) 2.97E+03 A
    b) 3.26E+03 A
    c) 3.57E+03 A
    d) 3.92E+03 A
    e) 4.30E+03 A
14) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 47A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,9) to the point (9,0).
    a) 8.91E+00 amps
    b) 9.77E+00 amps
    c) 1.07E+01 amps
    d) 1.18E+01 amps
    e) 1.29E+01 amps
15) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?
    a) 3.07E-04 s
    b) 3.71E-04 s
    c) 4.50E-04 s
    d) 5.45E-04 s
    e) 6.61E-04 s

### KEY:PhysicsCalc2:FE:V0

PhysicsCalc2152657831440
1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a$^2$, where β equals
    -a) 1.52 x 10$^{-4}$ unit
    -b) 1.85 x 10$^{-4}$ unit
    +c) 2.24 x 10$^{-4}$ unit
    -d) 2.71 x 10$^{-4}$ unit
    -e) 3.28 x 10$^{-4}$ unit
2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$
    -a) 3
    -b) 1/2
    -c) 2
    +d) 3/2
3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    -a) $2R\varepsilon _{0}E=r^{2}\rho$
    -b) $2\varepsilon _{0}E=r\rho$
    -c) none of these are correct
    -d) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    +e) $2r\varepsilon _{0}E=R^{2}\rho$
4) A parallel plate capacitor has both plates with an area of 1.35 m$^2$. The separation between the plates is 1.23mm. Applied to the plates is a potential difference of 2.65 kV. What is the capacitance?
    -a) 7.35 nF.
    -b) 8.45 nF.
    +c) 9.72 nF.
    -d) 11.18 nF.
    -e) 12.85 nF.
5) What voltage is required accelerate an electron at rest to a speed of 7.6 x 10$^7$ m/s?
    -a) 3.2 x 10$^3$ volts
    -b) 4.9 x 10$^3$ volts
    -c) 7.3 x 10$^3$ volts
    -d) 1.1 x 10$^4$ volts
    +e) 1.6 x 10$^4$ volts
6) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(1.89+1.31z)\rho ^{3}{\hat {\rho }}+8.35z^{2}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    -a) 5.311E+02
    -b) 6.434E+02
    -c) 7.795E+02
    +d) 9.444E+02
    -e) 1.144E+03
7) The diameter of a copper wire is 9.9 mm, and it carries a current of 41 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    -a) 2.24 x 10$^{-5}$m/s
    -b) 2.72 x 10$^{-5}$m/s
    -c) 3.29 x 10$^{-5}$m/s
    +d) 3.99 x 10$^{-5}$m/s
    -e) 4.83 x 10$^{-5}$m/s
8) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?
    +a) ${\frac {6}{11}}\Omega$.
    -b) ${\frac {6}{3}}\Omega$.
    -c) ${\frac {11}{6}}\Omega$.
    -d) ${\frac {3}{6}}\Omega$.
9) A 5.8 ohm resistor is connected in series to a pair of 2.8 ohm resistors that are in parallel. What is the net resistance?
    +a) 7.2 ohms.
    -b) 8.3 ohms.
    -c) 9.5 ohms.
    -d) 11 ohms.
    -e) 12.6 ohms.
10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?
    -a) 1.3 x 10$^2$ m.
    -b) 4.1 x 10$^2$ m.
    -c) 1.3 x 10$^3$ m.
    -d) 4.1 x 10$^3$ m.
    +e) 1.3 x 10$^4$ m.
11) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?
    -a) 5.43 x 10$^0$ volts
    +b) 6.58 x 10$^0$ volts
    -c) 7.97 x 10$^0$ volts
    -d) 9.65 x 10$^0$ volts
    -e) 1.17 x 10$^1$ volts
12) An object is placed 3.55 cm to the left of a converging lens with a focal length of 6.8 cm. How far is the image from the lens?
    -a) 4.18 x 10$^0$ cm
    +b) 7.43 x 10$^0$ cm
    -c) 1.32 x 10$^1$ cm
    -d) 2.35 x 10$^1$ cm
    -e) 4.18 x 10$^1$ cm
13) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$\int {\vec {H}}\cdot {\vec {d\ell }}$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?
    -a) 2.97E+03 A
    -b) 3.26E+03 A
    +c) 3.57E+03 A
    -d) 3.92E+03 A
    -e) 4.30E+03 A
14) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 47A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,9) to the point (9,0).
    -a) 8.91E+00 amps
    -b) 9.77E+00 amps
    -c) 1.07E+01 amps
    +d) 1.18E+01 amps
    -e) 1.29E+01 amps
15) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?
    -a) 3.07E-04 s
    -b) 3.71E-04 s
    +c) 4.50E-04 s
    -d) 5.45E-04 s
    -e) 6.61E-04 s

### PhysicsCalc2:FE:V1

PhysicsCalc2152657831440
1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$
    a) 3
    b) 3/2
    c) 2
    d) 1/2
2) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?
    a) 1.3 x 10$^2$ m.
    b) 4.1 x 10$^2$ m.
    c) 1.3 x 10$^3$ m.
    d) 4.1 x 10$^3$ m.
    e) 1.3 x 10$^4$ m.
3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    a) $2r\varepsilon _{0}E=R^{2}\rho$
    b) none of these are correct
    c) $2R\varepsilon _{0}E=r^{2}\rho$
    d) $2\varepsilon _{0}E=r\rho$
    e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
4) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 43A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,7.1) to the point (7.1,0).
    a) 8.15E+00 amps
    b) 8.94E+00 amps
    c) 9.80E+00 amps
    d) 1.08E+01 amps
    e) 1.18E+01 amps
5) The diameter of a copper wire is 9.9 mm, and it carries a current of 41 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    a) 2.24 x 10$^{-5}$m/s
    b) 2.72 x 10$^{-5}$m/s
    c) 3.29 x 10$^{-5}$m/s
    d) 3.99 x 10$^{-5}$m/s
    e) 4.83 x 10$^{-5}$m/s
6) A parallel plate capacitor has both plates with an area of 0.75 m$^2$. The separation between the plates is 0.53mm. Applied to the plates is a potential difference of 3.55 kV. What is the capacitance?
    a) 7.16 nF.
    b) 8.24 nF.
    c) 9.47 nF.
    d) 10.9 nF.
    e) 12.53 nF.
7) What voltage is required accelerate an electron at rest to a speed of 3 x 10$^5$ m/s?
    a) 1.7 x 10$^{-1}$ volts
    b) 2.6 x 10$^{-1}$ volts
    c) 3.8 x 10$^{-1}$ volts
    d) 5.8 x 10$^{-1}$ volts
    e) 8.6 x 10$^{-1}$ volts
8) A very long and thin solenoid has 2994 turns and is 180 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$\int {\vec {H}}\cdot {\vec {d\ell }}$ along an on-axis path that starts 43 meters from the center and stops 101 meters from the center?
    a) 6.63E+03 A
    b) 7.27E+03 A
    c) 7.97E+03 A
    d) 8.74E+03 A
    e) 9.58E+03 A
9) An object is placed 6.55 cm to the left of a converging lens with a focal length of 5.4 cm. How far is the image from the lens?
    a) 3.08 x 10$^0$ cm
    b) 5.47 x 10$^0$ cm
    c) 9.73 x 10$^0$ cm
    d) 1.73 x 10$^1$ cm
    e) 3.08 x 10$^1$ cm
10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a$^2$, where β equals
    a) 2.22 x 10$^{-3}$ unit
    b) 2.69 x 10$^{-3}$ unit
    c) 3.26 x 10$^{-3}$ unit
    d) 3.95 x 10$^{-3}$ unit
    e) 4.79 x 10$^{-3}$ unit
11) A 7 ohm resistor is connected in series to a pair of 3.4 ohm resistors that are in parallel. What is the net resistance?
    a) 6.6 ohms.
    b) 7.6 ohms.
    c) 8.7 ohms.
    d) 10 ohms.
    e) 11.5 ohms.
12) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?
    a) 6.34 x 10$^{-1}$ volts
    b) 7.68 x 10$^{-1}$ volts
    c) 9.31 x 10$^{-1}$ volts
    d) 1.13 x 10$^0$ volts
    e) 1.37 x 10$^0$ volts
13) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    a) 4.489E+02
    b) 5.438E+02
    c) 6.589E+02
    d) 7.983E+02
    e) 9.671E+02
14) A circlular capactitor of radius 4.6 m has a gap of 7 mm, and a charge of 18 μC. The capacitor is discharged through a 9 kΩ resistor. What is the decay time?
    a) 6.25E-04 s
    b) 7.57E-04 s
    c) 9.17E-04 s
    d) 1.11E-03 s
    e) 1.35E-03 s
15) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?
    a) ${\frac {3}{6}}\Omega$.
    b) ${\frac {11}{6}}\Omega$.
    c) ${\frac {6}{11}}\Omega$.
    d) ${\frac {6}{3}}\Omega$.

### KEY:PhysicsCalc2:FE:V1

PhysicsCalc2152657831440
1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$
    -a) 3
    +b) 3/2
    -c) 2
    -d) 1/2
2) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?
    -a) 1.3 x 10$^2$ m.
    -b) 4.1 x 10$^2$ m.
    -c) 1.3 x 10$^3$ m.
    -d) 4.1 x 10$^3$ m.
    +e) 1.3 x 10$^4$ m.
3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    +a) $2r\varepsilon _{0}E=R^{2}\rho$
    -b) none of these are correct
    -c) $2R\varepsilon _{0}E=r^{2}\rho$
    -d) $2\varepsilon _{0}E=r\rho$
    -e) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
4) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 43A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,7.1) to the point (7.1,0).
    -a) 8.15E+00 amps
    -b) 8.94E+00 amps
    -c) 9.80E+00 amps
    +d) 1.08E+01 amps
    -e) 1.18E+01 amps
5) The diameter of a copper wire is 9.9 mm, and it carries a current of 41 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    -a) 2.24 x 10$^{-5}$m/s
    -b) 2.72 x 10$^{-5}$m/s
    -c) 3.29 x 10$^{-5}$m/s
    +d) 3.99 x 10$^{-5}$m/s
    -e) 4.83 x 10$^{-5}$m/s
6) A parallel plate capacitor has both plates with an area of 0.75 m$^2$. The separation between the plates is 0.53mm. Applied to the plates is a potential difference of 3.55 kV. What is the capacitance?
    -a) 7.16 nF.
    -b) 8.24 nF.
    -c) 9.47 nF.
    -d) 10.9 nF.
    +e) 12.53 nF.
7) What voltage is required accelerate an electron at rest to a speed of 3 x 10$^5$ m/s?
    -a) 1.7 x 10$^{-1}$ volts
    +b) 2.6 x 10$^{-1}$ volts
    -c) 3.8 x 10$^{-1}$ volts
    -d) 5.8 x 10$^{-1}$ volts
    -e) 8.6 x 10$^{-1}$ volts
8) A very long and thin solenoid has 2994 turns and is 180 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$\int {\vec {H}}\cdot {\vec {d\ell }}$ along an on-axis path that starts 43 meters from the center and stops 101 meters from the center?
    -a) 6.63E+03 A
    +b) 7.27E+03 A
    -c) 7.97E+03 A
    -d) 8.74E+03 A
    -e) 9.58E+03 A
9) An object is placed 6.55 cm to the left of a converging lens with a focal length of 5.4 cm. How far is the image from the lens?
    -a) 3.08 x 10$^0$ cm
    -b) 5.47 x 10$^0$ cm
    -c) 9.73 x 10$^0$ cm
    -d) 1.73 x 10$^1$ cm
    +e) 3.08 x 10$^1$ cm
10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a$^2$, where β equals
    -a) 2.22 x 10$^{-3}$ unit
    +b) 2.69 x 10$^{-3}$ unit
    -c) 3.26 x 10$^{-3}$ unit
    -d) 3.95 x 10$^{-3}$ unit
    -e) 4.79 x 10$^{-3}$ unit
11) A 7 ohm resistor is connected in series to a pair of 3.4 ohm resistors that are in parallel. What is the net resistance?
    -a) 6.6 ohms.
    -b) 7.6 ohms.
    +c) 8.7 ohms.
    -d) 10 ohms.
    -e) 11.5 ohms.
12) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?
    -a) 6.34 x 10$^{-1}$ volts
    -b) 7.68 x 10$^{-1}$ volts
    -c) 9.31 x 10$^{-1}$ volts
    +d) 1.13 x 10$^0$ volts
    -e) 1.37 x 10$^0$ volts
13) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    -a) 4.489E+02
    -b) 5.438E+02
    -c) 6.589E+02
    -d) 7.983E+02
    +e) 9.671E+02
14) A circlular capactitor of radius 4.6 m has a gap of 7 mm, and a charge of 18 μC. The capacitor is discharged through a 9 kΩ resistor. What is the decay time?
    -a) 6.25E-04 s
    +b) 7.57E-04 s
    -c) 9.17E-04 s
    -d) 1.11E-03 s
    -e) 1.35E-03 s
15) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?
    -a) ${\frac {3}{6}}\Omega$.
    -b) ${\frac {11}{6}}\Omega$.
    +c) ${\frac {6}{11}}\Omega$.
    -d) ${\frac {6}{3}}\Omega$.

### PhysicsCalc2:FE:V2

PhysicsCalc2152657831440
1) An object is placed 3.15 cm to the left of a converging lens with a focal length of 6.7 cm. How far is the image from the lens?
    a) 3.34 x 10$^0$ cm
    b) 5.95 x 10$^0$ cm
    c) 1.06 x 10$^1$ cm
    d) 1.88 x 10$^1$ cm
    e) 3.34 x 10$^1$ cm
2) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 μC. The capacitor is discharged through a 5 kΩ resistor. What is the decay time?
    a) 2.57E-04 s
    b) 3.11E-04 s
    c) 3.77E-04 s
    d) 4.57E-04 s
    e) 5.53E-04 s
3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    b) $2\varepsilon _{0}E=r\rho$
    c) $2R\varepsilon _{0}E=r^{2}\rho$
    d) $2r\varepsilon _{0}E=R^{2}\rho$
    e) none of these are correct
4) A very long and thin solenoid has 2219 turns and is 134 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of$\int {\vec {H}}\cdot {\vec {d\ell }}$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?
    a) 2.41E+03 A
    b) 2.64E+03 A
    c) 2.89E+03 A
    d) 3.17E+03 A
    e) 3.48E+03 A
5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a$^2$, where β equals
    a) 1.61 x 10$^{-3}$ unit
    b) 1.95 x 10$^{-3}$ unit
    c) 2.36 x 10$^{-3}$ unit
    d) 2.86 x 10$^{-3}$ unit
    e) 3.46 x 10$^{-3}$ unit
6) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    a) 1.362E+03
    b) 1.650E+03
    c) 2.000E+03
    d) 2.423E+03
    e) 2.935E+03
7) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,8.4) to the point (8.4,0).
    a) 1.63E+01 amps
    b) 1.78E+01 amps
    c) 1.95E+01 amps
    d) 2.14E+01 amps
    e) 2.35E+01 amps
8) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?
    a) ${\frac {6}{3}}\Omega$.
    b) ${\frac {3}{6}}\Omega$.
    c) ${\frac {6}{11}}\Omega$.
    d) ${\frac {11}{6}}\Omega$.
9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$
    a) 3
    b) 2
    c) 3/2
    d) 1/2
10) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?
    a) 5.43 x 10$^0$ volts
    b) 6.58 x 10$^0$ volts
    c) 7.97 x 10$^0$ volts
    d) 9.65 x 10$^0$ volts
    e) 1.17 x 10$^1$ volts
11) What voltage is required accelerate an electron at rest to a speed of 7.6 x 10$^7$ m/s?
    a) 3.2 x 10$^3$ volts
    b) 4.9 x 10$^3$ volts
    c) 7.3 x 10$^3$ volts
    d) 1.1 x 10$^4$ volts
    e) 1.6 x 10$^4$ volts
12) The diameter of a copper wire is 1.9 mm, and it carries a current of 33 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    a) 5.93 x 10$^{-4}$m/s
    b) 7.19 x 10$^{-4}$m/s
    c) 8.71 x 10$^{-4}$m/s
    d) 1.06 x 10$^{-3}$m/s
    e) 1.28 x 10$^{-3}$m/s
13) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?
    a) 1.3 x 10$^2$ m.
    b) 4.1 x 10$^2$ m.
    c) 1.3 x 10$^3$ m.
    d) 4.1 x 10$^3$ m.
    e) 1.3 x 10$^4$ m.
14) A 6.6 ohm resistor is connected in series to a pair of 6.4 ohm resistors that are in parallel. What is the net resistance?
    a) 6.4 ohms.
    b) 7.4 ohms.
    c) 8.5 ohms.
    d) 9.8 ohms.
    e) 11.3 ohms.
15) A parallel plate capacitor has both plates with an area of 1.45 m$^2$. The separation between the plates is 0.93mm. Applied to the plates is a potential difference of 4.45 kV. What is the capacitance?
    a) 12 nF.
    b) 13.8 nF.
    c) 15.88 nF.
    d) 18.26 nF.
    e) 21 nF.

### KEY:PhysicsCalc2:FE:V2

PhysicsCalc2152657831440
1) An object is placed 3.15 cm to the left of a converging lens with a focal length of 6.7 cm. How far is the image from the lens?
    -a) 3.34 x 10$^0$ cm
    +b) 5.95 x 10$^0$ cm
    -c) 1.06 x 10$^1$ cm
    -d) 1.88 x 10$^1$ cm
    -e) 3.34 x 10$^1$ cm
2) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 μC. The capacitor is discharged through a 5 kΩ resistor. What is the decay time?
    +a) 2.57E-04 s
    -b) 3.11E-04 s
    -c) 3.77E-04 s
    -d) 4.57E-04 s
    -e) 5.53E-04 s
3) A cylinder of radius, R, and height H has a uniform charge density of $\rho$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
    -a) $2r^{2}\varepsilon _{0}E=R^{3}\rho$
    -b) $2\varepsilon _{0}E=r\rho$
    -c) $2R\varepsilon _{0}E=r^{2}\rho$
    +d) $2r\varepsilon _{0}E=R^{2}\rho$
    -e) none of these are correct
4) A very long and thin solenoid has 2219 turns and is 134 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of$\int {\vec {H}}\cdot {\vec {d\ell }}$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?
    -a) 2.41E+03 A
    -b) 2.64E+03 A
    +c) 2.89E+03 A
    -d) 3.17E+03 A
    -e) 3.48E+03 A
5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a$^2$, where β equals
    +a) 1.61 x 10$^{-3}$ unit
    -b) 1.95 x 10$^{-3}$ unit
    -c) 2.36 x 10$^{-3}$ unit
    -d) 2.86 x 10$^{-3}$ unit
    -e) 3.46 x 10$^{-3}$ unit
6) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, ${\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}$ Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate , $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$ over the top surface of the cylinder.
    -a) 1.362E+03
    -b) 1.650E+03
    +c) 2.000E+03
    -d) 2.423E+03
    -e) 2.935E+03
7) H is defined by, B=μ$_0$H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $\int {\vec {H}}\cdot {\vec {d\ell }}$, from the point (0,8.4) to the point (8.4,0).
    -a) 1.63E+01 amps
    -b) 1.78E+01 amps
    -c) 1.95E+01 amps
    -d) 2.14E+01 amps
    +e) 2.35E+01 amps
8) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?
    -a) ${\frac {6}{3}}\Omega$.
    -b) ${\frac {3}{6}}\Omega$.
    +c) ${\frac {6}{11}}\Omega$.
    -d) ${\frac {11}{6}}\Omega$.
9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$
    -a) 3
    -b) 2
    +c) 3/2
    -d) 1/2
10) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?
    -a) 5.43 x 10$^0$ volts
    +b) 6.58 x 10$^0$ volts
    -c) 7.97 x 10$^0$ volts
    -d) 9.65 x 10$^0$ volts
    -e) 1.17 x 10$^1$ volts
11) What voltage is required accelerate an electron at rest to a speed of 7.6 x 10$^7$ m/s?
    -a) 3.2 x 10$^3$ volts
    -b) 4.9 x 10$^3$ volts
    -c) 7.3 x 10$^3$ volts
    -d) 1.1 x 10$^4$ volts
    +e) 1.6 x 10$^4$ volts
12) The diameter of a copper wire is 1.9 mm, and it carries a current of 33 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m$^3$ and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
    -a) 5.93 x 10$^{-4}$m/s
    -b) 7.19 x 10$^{-4}$m/s
    +c) 8.71 x 10$^{-4}$m/s
    -d) 1.06 x 10$^{-3}$m/s
    -e) 1.28 x 10$^{-3}$m/s
13) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?
    -a) 1.3 x 10$^2$ m.
    -b) 4.1 x 10$^2$ m.
    -c) 1.3 x 10$^3$ m.
    -d) 4.1 x 10$^3$ m.
    +e) 1.3 x 10$^4$ m.
14) A 6.6 ohm resistor is connected in series to a pair of 6.4 ohm resistors that are in parallel. What is the net resistance?
    -a) 6.4 ohms.
    -b) 7.4 ohms.
    -c) 8.5 ohms.
    +d) 9.8 ohms.
    -e) 11.3 ohms.
15) A parallel plate capacitor has both plates with an area of 1.45 m$^2$. The separation between the plates is 0.93mm. Applied to the plates is a potential difference of 4.45 kV. What is the capacitance?
    -a) 12 nF.
    +b) 13.8 nF.
    -c) 15.88 nF.
    -d) 18.26 nF.
    -e) 21 nF.