Electrostatics

## Charge

Charge is quantized .

Q = ne

Law of Conservation of Charge = Charge can neither be created nor be destroyed , it can only be transferred from one body to another .

## Coulomb's Law

When two charges , touch each other , the charge is equally shared by them . The electrostatic force inside a conductor is zero .

F = k q1q2 / r2

where k = 1 / 4πε = 9 x 109 Nm2/C2

## Charge Density

λ = Q/l

σ = Q/A

ρ = Q/V

## Electric Field Intensity

E = F/Q

E = k q / r2 (due to point charge)

**Due to Dipole : E = k psinθ / r3**

**Inside a Conductor :** k = infinite ... E = 0

Note : Potential decreases in the direction of Electric Field Intensity .

**Due to Conductor of length L and at distance a :**

E = k q / r [1/a - 1/(L+a)]

**Non-Conducting Sphere :**

The Electric Field Intnsity inside and outsid a non-conductor aries just like g varies wih depth and height .

## Electric Lines of Force

1. No two electric lines of force can intersect each other , they are always parallel .
2. Electric Lines of Force are close continuous curves and they start from positive and end on negative charge .
3. The tangent drawn at any instant to the lines of force , gives it direction at that instant .
4. The lines are more crowded where the field is strong and less crowded where the field is weak .
5. When two unlike charges are placed close to each other , the lines of force are compressed ; this explains attraction of unlike charges .
6. When two like charges are placed close to each other , the lines of force exert lateral pressure on each other , this explains repulsion of like charges .

## Electric Potential Energy

U = F.r = k q1q2/r

**Potential Energy of System of Charges :**

 U = U1 + U2 + U3 +.......+ Un

**Potential Energy of Dipole in an External Field :**

U = -pEcosθ

Wor done in rotating a dipole from θ1 to θ2 = - pE (cosθ1 - cos θ2)

## Electric Potential

V = U/q = F.r / q = k q/r

V = Er = U/Q

... U = VQ

The sign of Potential depends on like/unlike charges .

**Cases of Potential :**

1. **Due to point charge :** V = - kq/r ... at r = 0 , Z is negative infinite . The graph will be negative , curved and parallel to V and r axes .
2. **Inside a Solid Sphere :** V = - kq (1.5R2 - 0.5r2) / R3 . At r=R ,V = - kq**/**R . At r = 0 ,V = -1.5kq**/**R The graph is negative , parabolic .
3. **Outside a Solid Sphere :** V = -kq/r , at r = infinity , V = 0 ; On surface , V = -kq/R
4. **Due to a Spherical Shell :** Outside V = -kq/r . Inside V = - kq/r
5. **On the Axis of a Ring :** V = - kq / sqrt(R2+x2)

**Due to Dipole : V = k pcosθ / r2**

At an equatorial point , the electric potential is zero

Note : Potential decreases in the direction of Electric Field Intensity .

## Common Potential

Suppose two spheres of radii r1 & r2 are connected by a wire and charges q1 & q2 are residing on their surfaces

then Common Potential = [q1 + q2] / 4πε(r1+r2)

## Gauss' Theorem

NEI = εE

TNEI = ∫ NEI = ∫ εE dscosθ

**The** **Gauss's Law** states that the Total Normal Electric Induction is equal to the algebraic sum of the Charges enclosed by the surface .

**TNEI = Qi**

## Applications of Gauss's Law

1. Sphere : E = 1 / 4πε0 q/r2
2. Cylinder : E = λ/2πε0r
3. Any Shape : E = *σ*/*ε0*
4. Sheet : E = *σ*/2*ε0*

## Mechanical Force

Mechanical Force per Unit Area = 1/2 E2ε = 1/2 *σ2/ε*

## Energy Density

Potential Energy per unit Volume = 1/2 E2ε = 1/2 *σ2/ε*

## Dielectrics and Polarization

Polar

Non-Polar

Electric Moments

Polarization = P = σp {Amount of charge induced due to external electric field}

## Capacitance

Q = CV

C = Q/V

C = Aε / d

**Series Combination :**

Cs = 1/C1 + 1/C2 + 1/C3 + .... +1/Cn

**Parallel Combination :**

Cp = C1 + C2 + C3 + .... + Cn

**Energy Stored in a Capacitor :**

E = 1/2 CV2

**Force between the plates of Capacitor :**

F = Q2 / 2Aε

C = kCo

## Tips and Tricks

1) For repulsive force between two like charges , the closest distance of approach is when Kinetic Energy is equal to Potential Energy .

2) For questions related to Flux and Electric Field Intensity , consider **Gauss Theorem** .

The formulae for E , at diffrent distances from a conductor , circuar conductor and at centre of circular conductor is the sam as B .