MikaStars39/nano-eval huggingface dataset:
What period did Goliath appear in?

Options:
A. During the democratization of knowledge, the spread of maritime navigation, after metal trade routes stabilized, and before advanced colonial systems.
B. During the invention of algebra in Baghdad, the display of baroque artistry, well after papyrus was deducted, and before the Great Plague reached.
C. During the period of ancient art, the period of new art, before the establishment of formal universities in Europe, and after the French troubadours.
D. During turbulent astral religious shifts, growth of feudal land ownership, after nomadic invasions dissipated, and before postmodern shifts.
E. During conflicts between eastern city-states, the philosophical age of Confucian revival, while dynastic shifts were prevalent, and amid lost wander periods.
F. During the Bronze Age of Mesopotamia, the height of Mayan civilization, before the industrial societies rose, and amid the Viking conquests.
G. During the launch of age exploration, the Enlightenment's academic boom, after the printing press spread, and before modern capitalism grew.
H. During the rise of classical philosophy, the Renaissance's early stages, after medieval scholasticism declined, and amid the Baroque minimalism shift.
I. During the rule of the Roman Republic, the Golden Age of Athens, after the fall of Troy, and before the reign of Charlemagne.
J. During the development of Gothic architecture, the era of romantic poetry, while steam engines were invented, and after the discovery of electricity.
Answer: C
What are the two types of Italian oratorios?

Options:
A. Liturgical Cantatas and Secular Chorales
B. Operatic Oratorios and Lyric Cantatas
C. Pastoral Oratorios and Italian Motets
D. Latin Oratorios and Secular Oratorios
E. Sacred Chorales and Serenatas
F. Liturgical Oratorios and Roman Oratorios
G. Sacred Operas and Dramatic Cantatas
H. Baroque Cantatas and Religious Serenatas
I. Vocal Suites and Church Madrigals
J. Vernacular Oratorios and Choral Cantatas
Answer: D
What is the basis of a grand concerto?

Options:
A. Union Between Multiple Ensembles in Symphonic Form.
B. Harmony Between All Instrument Groups Over Time.
C. Transition Between Solo Piano and Supporting String Sections.
D. Contrast Between Small Ensemble Solo Instruments and Large Ensemble Instruments.
E. Connection Between Rhythmic Patterns and Orchestra Layers.
F. Coordination Between All Voices and Choral Movements.
G. Integration Between Stage Performance and Ensemble Players.
H. Interaction Between Different Thematic Melodic Lines Throughout.
I. Alternation Between Different Instrument Sections and Choirs.
J. Cooperation Between Virtuoso Performers and Full Orchestra.
Answer: D
Which predecessor's stylistic characteristics did German composer Richard Strauss follow in his symphonic music with programmatic titles?

Options:
A. Mozart
B. Haydn
C. Tchaikovsky
D. Mendelssohn
E. Mahler
F. Schubert
G. Berlioz
H. Beethoven
I. Wagner
J. Brahms
Answer: I
Which of Puccini's operas are named after the female protagonists?

Options:
A. "La Bohème"; "Turandot"; "Manon Lescaut"; "Sister Angelica".
B. "Tosca"; "Turandot"; "La Rondine"; "Sister Angelica".
C. "Tosca"; "Turandot"; "Madama Butterfly"; "Sister Angelica".
D. "Madama Butterfly"; "Tosca"; "Turandot"; "Sister Angelica".
E. "Manon Lescaut"; "Tosca"; "Turandot"; "Madama Butterfly".
F. "Manon Lescaut"; "Turandot"; "Tosca"; "La Rondine".
G. "Tosca"; "Turandot"; "Manon Lescaut"; "Sister Angelica".
H. "Tosca"; "Turandot"; "Edgar"; "Sister Angelica".
I. "La Bohème"; "Tosca"; "Turandot"; "Sister Angelica".
J. "Tosca"; "Turandot"; "Il Tabarro"; "Sister Angelica".
Answer: G
Why is total serialism music also called integral serialism music?

Options:
A. Building upon the foundation of the twelve tones, expansions were made to tonalities; unique key centers were explored.
B. Building upon the foundation of the twelve tones, further developments were made; various phonemes were arranged into different sequences.
C. Building upon the foundation of the twelve tones, reinterpretations centered on texture; layering achieved prominence.
D. Building upon the foundation of the twelve tones, composers altered formats; specific movements were eliminated.
E. Building upon the foundation of the twelve tones, composers redefined harmony; dissonance was deliberately highlighted.
F. Building upon the foundation of the twelve tones, additional techniques emerged; instrumentation choices were prioritized.
G. Building upon the foundation of the twelve tones, additional focus was given to dynamics; composers assigned specific volumes.
H. Building upon the foundation of the twelve tones, further developments emphasized rhythm; distinct patterns were implemented.
I. Building upon the foundation of the twelve tones, additional approaches included silence; rests gained structural significance.
J. Building upon the foundation of the twelve tones, further developments reshaped melodies; simpler motifs became popular.
Answer: B
In the practice of rotation between paddy and dry land, phosphate fertilization should ______.

Options:
A. Promote Constant Paddy Production
B. Focus Solely on Wetland Farming
C. Be Increased in Dryland Areas Only
D. Encourage Exclusive Phosphate Application
E. Support Both Paddy and Dryland Equally
F. Enhance Growth in Paddy Cultivation
G. Reduce Its Use in Wetland Farming
H. Occur Only During Paddy Harvest Phase
I. Priority Given to Dryland Cultivation
J. Align with Seasonal Water Availability
Answer: I
The newly discovered dwarf planet', Eris, has an elliptical orbit with a semi-major axis of 67.89 AU. Calculate its period in years.

Options:
A. $$\mathrm{623.7years}$$
B. $$\mathrm{512.8years}$$
C. $$\mathrm{490.6years}$$
D. $$\mathrm{578.5years}$$
E. $$\mathrm{461.2years}$$
F. $$\mathrm{559.4years}$$
G. $$\mathrm{600.3years}$$
H. $$\mathrm{560.8years}$$
I. $$\mathrm{447.1years}$$
J. $$\mathrm{539.9years}$$
Answer: F
Following the summer exams, two astrophysics students had been sunbathing on a flat beach in Sweden (latitude: $+ 6 2^{\circ}$ ) at 12:00 Local Solar Time on June 21. In the evening, the students decided to estimate the number of neutrinos per second passing through their bodies that morning. Their lecture notes told them that the Earth's axis is tilted at $\mathrm{23.5^{\circ}}$ to the plane of the ecliptic, the solar constant was $\sim 1 3 0 0 \, \mathrm{W} \, \mathrm{m}^{-2}$, that one proton-proton cycle converted $4. 6 \times1 0^{-2 9}$ kg of mass into energy and they knew that the velocity of light is $3 \times1 0^{8} \mathrm{m s}^{-1}$ . The students
realised that it was not necessary to know how far the Earth was from the Sun and quickly came up with a result. What might the result have been, assuming that the cross-sectional area of a prone student was $1 \mathrm{m}^{2}$? (Note: you can get a pretty good result ignoring where and when they were, but some of you might like to give a more accurate result. If the Earth's equator was in the plane of the Solar System, the Sun would remain at declination zero. Given a tilt of the Earth's rotation axis of $\theta^{\circ}$ , the Sun's declination will vary between $+ \theta^{\circ}$ and $- \theta^{\circ}$ over the year.)

Options:
A. $$
5. 2 0 0 \times1 0^{1 4}
$$
B. $$
6. 3 3 4 \times1 0^{1 4}
$$
C. $$
4. 7 5 0 \times1 0^{1 2}
$$
D. $$
5. 8 4 1 \times1 0^{1 4}
$$
E. $$
6. 0 0 0 \times1 0^{1 3}
$$
F. $$
3. 8 7 9 \times1 0^{1 3}
$$
G. $$
3. 9 2 5 \times1 0^{1 4}
$$
H. $$
2. 4 6 1 \times1 0^{1 5}
$$
I. $$
4. 1 0 2 \times1 0^{1 5}
$$
J. $$
4. 9 1 5 \times1 0^{1 4}
$$
Answer: J
The radial velocity of a 1 solar mass star is seen to vary sinusoidally by $+ /-3 0 \, \mathrm{m \cdot s^{-1}}$ with a period of 1460 days. Assuming that the Earth lay in the plane of the orbit of the object causing this stellar motion, calculate its mass in Jovian masses. (Assume that the simple form of Kepler's Third Law is valid, where $P^{2}=R^{3}$ when $P$ is in years and $R$ is in AU. $1 \mathrm{~ A U}=1. 4 9 \times1 0^{1 1} \mathrm{m}$ , and Jupiter is 0.001 solar masses.)

Options:
A. $$1. 4 1 M_{J}$$
B. $$1. 8 2 M_{J}$$
C. $$1. 7 6 M_{J}$$
D. $$2. 1 0 M_{J}$$
E. $$0. 9 8 M_{J}$$
F. $$1. 1 4 M_{J}$$
G. $$2. 5 6 M_{J}$$
H. $$1. 6 9 M_{J}$$
I. $$2. 0 3 M_{J}$$
J. $$1. 5 7 M_{J}$$
Answer: J
A Newtonian telescope has a mirror diameter of 300 mm and a focal length of 1 500mm. The tube has an external diameter of 330 mm and the focal plane is 40 mm outside the tube. What tolerance in the manufacture of the mirror surface would you need if the maximum phase error were not to exceed $\frac{1}{6} \lambda$ at this wavelength?

Options:
A. 49.6nm
B. 50.3nm
C. 45.0nm
D. 39.2nm
E. 47.8nm
F. 44.3nm
G. 42.5nm
H. 30.5nm
I. 38.0nm
J. 41.0nm
Answer: G
A star has a radius and surface temperature that are both twice that of our Sun. What will be its radiated energy output compared with that of our Sun?

Options:
A. 16
B. 96
C. 256
D. 8
E. 48
F. 32
G. 72
H. 128
I. 64
J. 100
Answer: I
The Ring Nebula has an angular diameter of 72 arcsec. Given that it is at a distance of $\mathrm{\sim 1500 pc}$ and it is expanding at a velocity of $15\mathrm{km \cdot s}^{-1}$, estimate its age.

Options:
A. $$
2. 0 \times1 0^{4} y e a r s
$$
B. $$
8. 1 \times1 0^{4} y e a r s
$$
C. $$
1. 2 \times1 0^{6} y e a r s
$$
D. $$
4. 5 \times1 0^{5} y e a r s
$$
E. $$
7. 2 \times1 0^{4} y e a r s
$$
F. $$
1. 5 \times1 0^{5} y e a r s
$$
G. $$
1. 7 \times1 0^{4} y e a r s
$$
H. $$
9. 8 \times1 0^{3} y e a r s
$$
I. $$
3. 4 \times1 0^{4} y e a r s
$$
J. $$
6. 3 \times1 0^{5} y e a r s
$$
Answer: G
Accretion of supermassive objects surrounding the region of radiation Black holes vary a lot on 12-hour timescales. Knowing that it takes 8.32 light minutes for light to travel from the Sun to the Earth, what is the size of the region estimated in astronomical units (AU)?

Options:
A. $$
9 4. 3 \mathrm{A U}
$$
B. $$
8 9. 2 \mathrm{A U}
$$
C. $$
7 5. 9 \mathrm{A U}
$$
D. $$
7 4. 8 \mathrm{A U}
$$
E. $$
8 2. 7 \mathrm{A U}
$$
F. $$
8 6. 5 \mathrm{A U}
$$
G. $$
8 7. 3 \mathrm{A U}
$$
H. $$
9 1. 8 \mathrm{A U}
$$
I. $$
9 0. 6 \mathrm{A U}
$$
J. $$
7 8. 1 \mathrm{A U}
$$
Answer: F
The wave function of the electron in the hydrogen atom is given by $\Psi_{2 1 1}=\frac{1} {8 \sqrt{\pi}} ( \frac{1} {a_{1}} )^{\frac{3} {2}} ( \frac{r} {a_{1}} ) e^{\frac{r} {2a_{1}}} {sin \theta}e^{xp}$, where $a_{1}$ is the first Bohr radius.
Determine the radius of the shell where the probability of the electron appearing radially is maximized is _____.

Options:
A. $$
r=2a_{1}
$$
B. $$
r=6a_{1}
$$
C. $$
r=3a_{1}
$$
D. $$
r=\frac{3a_{1}}{2}
$$
E. $$
r=a_{1}
$$
F. $$
r=7a_{1}
$$
G. $$
r=8a_{1}
$$
H. $$
r=4a_{1}
$$
I. $$
r=\frac{5a_{1}}{3}
$$
J. $$
r=5a_{1}
$$
Answer: H
The $K$ absorption edge of tungsten is 0.0178 nm. The average wavelength of the $\mathbf{K}$ series $\lambda_{k_{\alpha}}$ is $0.0211 \, \mathrm{nm}$. $\lambda_{k_{\beta}}$ is $0.0184 \, \mathrm{nm}$, and $\lambda_{k_{\gamma}}$ is 0.0179 nm. If tungsten is irradiated with photons of 80 keV, what is the range of kinetic energy of electrons ejected from the $\mathrm{N}$ shell to $n=\infty$?

Options:
A. $$
78.8\sim79keV
$$
B. $$
75.2\sim76keV
$$
C. $$
39.2\sim40keV
$$
D. $$
18.4\sim19keV
$$
E. $$
10.1\sim11keV
$$
F. $$
79.6\sim80keV
$$
G. $$
15.0\sim16keV
$$
H. $$
0.3\sim0.4keV
$$
I. $$
20.8\sim22keV
$$
J. $$
43.5\sim44keV
$$
Answer: F
The electron configuration of the ground-state Ca (calcium) atom outside the nucleus is ${[Ar]4s^{2}}$, where one of the 4s electrons can be excited to 4p, 3d, 5s, and other orbitals, thereby forming singlet and triplet states. If a particular triplet state of Ca has energy levels that are higher than the ground state energy level by 20335.4 $cm^{-1}$, 20349.3 $cm^{-1}$, and 20371.0 $cm^{-1}$, what is the electron configuration that forms this triplet state?

Options:
A. 3p4s
B. 3d5s
C. 3d4f
D. 3d4p
E. 4s4p
F. 4p4d
G. 4s3d
H. 4p3d
I. 4s5p
J. 4s3p
Answer: G
The rotational constant of the $^{1}H^{35}Cl$ molecule, measured experimentally, is $B = 10.397 \ cm^{-1}$. The reduced mass of this molecule is $1.63 \times 10^{-27} \ kg$. What is the equilibrium distance between the two atoms in the HCl molecule?

Options:
A. 0.140nm
B. 0.135nm
C. 0.150nm
D. 0.121nm
E. 0.129nm
F. 0.156nm
G. 0.118nm
H. 0.167nm
I. 0.112nm
J. 0.143nm
Answer: E
An atomic nucleus with a mass of $M$ combines with an electron with a mass of $m_{e}$ to form a single-electron ion. What is the relationship between the Rydberg constant $R_{M}$ for this ion and $R_{\infty}$?

Options:
A. $$
R_{M}=R_{\infty} / ( 1-\frac{m_{e}} {M} ) \
$$
B. $$
R_{M}=R_{\infty} / ( \frac{M} {m_{e}} ) \
$$
C. $$
R_{M}=R_{\infty} \cdot ( 1-\frac{m_{e}} {M} ) \
$$
D. $$
R_{M}=R_{\infty} \cdot \frac{M} {( M+m_{e})} \
$$
E. $$
R_{M}=R_{\infty} / ( 1+\frac{M} {m_{e}} ) \
$$
F. $$
R_{M}=R_{\infty} \cdot ( \frac{M} {m_{e}} ) \
$$
G. $$
R_{M}=R_{\infty} / \frac{M} {( M-m_{e})} \
$$
H. $$
R_{M}=R_{\infty} / ( 1+\frac{m_{e}} {M} ) \
$$
I. $$
R_{M}=R_{\infty} \cdot ( 1+\frac{m_{e}} {M} ) \
$$
J. $$
R_{M}=R_{\infty} \cdot ( \frac{m_{e}} {M+m_{e}} ) \
$$
Answer: H
For a certain atom $\mathrm{^{1}D_{2}} \to {^{1}P_{1}}$, the spectral line of the transition will split in an external magnetic field. How many lines can be observed along the direction of the magnetic field?

Options:
A. 10
B. 1
C. 3
D. 6
E. 5
F. 8
G. 7
H. 2
I. 9
J. 4
Answer: H
The helium atom transitions from the state $1s2p {^{3}P_{2, 1, 0}}$ to $1s2s{^{3}S_{1}}$. How many spectral lines can be produced?

Options:
A. 9
B. 7
C. 4
D. 1
E. 0
F. 5
G. 6
H. 8
I. 2
J. 3
Answer: J
When preparing $Al_2O_3$ ceramics, if the raw material particle size is 2μm, and it is held at the sintering temperature for 30 minutes, the measured grain size is 10μm. Then, after holding at the sintering temperature for 2 hours, what will the grain size be in μm? To inhibit grain growth, 0.2% MgO is added to the raw material, and it is held at the same sintering temperature for 2 hours. What will the grain size be in μm?

Options:
A. 19μm,13μm
B. 25μm,18μm
C. 30μm,15μm
D. 17μm,15μm
E. 24μm,12μm
F. 26μm,18μm
G. 22μm,14μm
H. 23μm,20μm
I. 20μm,16μm
J. 21μm,17μm
Answer: I
Given a powder compact with an average particle size of 5 μm, after 2 hours of sintering, the neck growth rate is $x/r = 0.1$. If grain growth is not considered, calculate the time required to sinter the compact to a neck growth rate of $x/r = 0.2$ for each of the following mass transfer mechanisms: evaporation-condensation, diffusion, and dissolution-precipitation is ().

Options:
A. 10h,40h,80h
B. 14h,56h,112h
C. 16h,64h,128h
D. 12h,48h,96h
E. 12h,36h,108h
F. 25h,100h,200h
G. 18h,72h,144h
H. 20h,80h,160h
I. 15h,60h,120h
J. 22h,88h,176h
Answer: C
Under the condition of 1600°C , what is the diffusion behavior of $\mathrm{Mg}^{2+}$ in MgO crystals containing 1 part per million of $Al_2O_3$ impurities?
( the formation energy of Schottky defects in MgO crystals is $6 \, \mathrm{eV} = 9.612 \times 10^{-19} \, \mathrm{J}$, $k = 1.380 \times 10^{-23} \, \mathrm{J/K}$ )

Options:
A. Purely extrinsic conduction
B. Thermally enhanced migration
C. Non-intrinsic diffusion
D. Intrinsic conduction pathway
E. Mixed impurity diffusion
F. Lattice deformation independent
G. Dominant Schottky vacancies
H. Thermodynamic equilibrium achieved
I. Uniform ionic displacement
J. Homogeneous atom distribution
Answer: C
In large-scale motion systems, low pressure is combined with (), and the low-pressure center is the () center. Conversely, high pressure is combined with (), and the high-pressure center is the () center.

Options:
A. Anticyclonic circulation, cyclonic circulation, cyclonic circulation, anticyclonic circulation
B. Cyclonic center, cyclonic center, anticyclonic center, anticyclonic center
C. Opposite flow, cyclonic flow, matching flow, anticyclonic flow
D. Cyclonic activity, cyclonic center, anticyclonic activity, anticyclonic center
E. Anticyclonic motion, cyclonic motion, cyclonic motion, anticyclonic motion
F. Cyclonic circulation, anticyclonic circulation, cyclonic circulation, cyclonic circulation
G. Anticyclonic flow, anticyclonic flow, cyclonic flow, cyclonic flow
H. Cyclonic circulation, cyclonic circulation, anticyclonic circulation, anticyclonic circulation
I. Cyclonic flow, cyclonic flow, anticyclonic flow, anticyclonic flow
J. Rotational circulation, rotational circulation, counter-rotational circulation, counter-rotational circulation
Answer: H
The Paschen series of hydrogen( $n=3$ ) can contribute to the visible continuum for the Sun since the series limit occurs at 820.8 nm. However, it is the contribution from the $\mathrm{H^{-}}$ ion that dominates the formation of the continuum. Using $\frac{N_{\mathrm{H}}} {N_{\mathrm{H}}-}$=$5\times10^{7}$
, along with the Boltzmann equation, estimate the ratio of the number of $\mathrm{H^{-}}$ ions to hydrogen atoms in the $n=3$ state is ().

Options:
A. 96
B. 62
C. 67
D. 73
E. 56
F. 45
G. 94
H. 79
I. 82
J. 88
Answer: H
The frequency shift produced by the normal Zeeman effect in the center of a sunspot that has a magnetic field strength of 0.3 T is().

Options:
A. $$
6. 4 \times1 0^{9} \mathrm{~ H z}
$$
B. $$
4. 2 \times1 0^{9} \mathrm{~ H z}
$$
C. $$
8. 6 \times1 0^{8} \mathrm{~ H z}
$$
D. $$
1. 1 \times1 0^{9} \mathrm{~ H z}
$$
E. $$
5. 1 \times1 0^{9} \mathrm{~ H z}
$$
F. $$
3. 8 \times1 0^{8} \mathrm{~ H z}
$$
G. $$
9. 8 \times1 0^{8} \mathrm{~ H z}
$$
H. $$
4. 0 \times1 0^{8} \mathrm{~ H z}
$$
I. $$
7. 2 \times1 0^{9} \mathrm{~ H z}
$$
J. $$
2. 5 \times1 0^{8} \mathrm{~ H z}
$$
Answer: B
Assume that radar signals of 10 GHz are used to measure the rotation rates of Mercury and Venus. Using the Doppler effect, determine the relative shifts in frequency for signals returning from the approaching and receding limbs of each planet.

Options:
A. $$
1. 0 \times1 0^{-8}
$$
$$
1. 8 \times1 0^{-8}
$$
B. $$
1. 9 \times1 0^{-7}
$$
$$
1. 2 \times1 0^{-9}
$$
C. $$
9. 9 \times1 0^{-9}
$$
$$
1. 2 \times1 0^{-7}
$$
D. $$
1. 7 \times1 0^{-8}
$$
$$
2. 2 \times1 0^{-8}
$$
E. $$
2. 0 \times1 0^{-8}
$$
$$
1. 5 \times1 0^{-8}
$$
F. $$
1. 9 \times1 0^{-8}
$$
$$
1. 2 \times1 0^{-8}
$$
G. $$
1. 4 \times1 0^{-8}
$$
$$
1. 0 \times1 0^{-8}
$$
H. $$
1. 5 \times1 0^{-7}
$$
$$
3. 0 \times1 0^{-8}
$$
I. $$
0. 9 \times1 0^{-8}
$$
$$
1. 3 \times1 0^{-8}
$$
J. $$
1. 8 \times1 0^{-8}
$$
$$
1. 2 \times1 0^{-7}
$$
Answer: F
The moment of inertia of a planet is used to evaluate its interior structure. In this problem you will construct asimple two-zone modelof the interior of Earth, assuming spherical symmetry Take the average densities of the core and mantle to be 10,900 kg m $- 3$ and 4500 kg m" respectively (neglect the thin surface crust)
Using the average density of the entire Earth, determine the radius of the core. Express your answer in units of Earth's radius.

Options:
A. 0.44
B. 0.50
C. 0.56
D. 0.60
E. 0.54
F. 0.62
G. 0.58
H. 0.49
I. 0.52
J. 0.46
Answer: E
Calculate the position of Saturn's synchronous orbit. Are any of its rings located outside of that radius? If so, which ones?

Options:
A. $$
1. 14 \, \mathrm{R_{S}}.
$$
B. $$
1. 15 \, \mathrm{R_{S}}.
$$
C. $$
1. 13 \, \mathrm{R_{S}}.
$$
D. $$
1. 8 \, \mathrm{R_{S}}.
$$
E. $$
1. 7 \, \mathrm{R_{S}}.
$$
F. $$
1. 11 \, \mathrm{R_{S}}.
$$
G. $$
1. 6 \, \mathrm{R_{S}}.
$$
H. $$
1. 9 \, \mathrm{R_{S}}.
$$
I. $$
1. 12 \, \mathrm{R_{S}}.
$$
J. $$
1. 10 \, \mathrm{R_{S}}.
$$
Answer: H
In Problem 21.16, the Poynting-Robertson effect was shown to be important in understanding the dynamics of ring systems. The Poynting-Robertson effect, together with radiation pressure, is also important in clearing the Solar System of dust left behind by comets and colliding asteroids (the dust that is responsible for the zodiacal Beginning with Eq. (21.6), found in Problem 21 . 15, show that the time required for a spher-
ical particle of radius $R$ and density $\rho$ to spiral into the Sun from an initial orbital radius
of $r \gg R_{\odot}$ is given by Eq. (22.4). Assume that the orbit of the dust grain is approximately
circular at all times.

Options:
A. $$
-\frac{L_{\odot} R^{2}} {2 c^{2} R_{\odot}} t \mathrm{s u n}.
$$
B. $$
-\frac{R^{2}} {2 m c L_{\odot}} t \mathrm{s u n}.
$$
C. $$
-\frac{L_{\odot}} {2 R m c^{2}} t \mathrm{s u n}.
$$
D. $$
-\frac{L_{\odot} R} {m c^{3}} t \mathrm{s u n}.
$$
E. $$
-\frac{L_{\odot} R^{2}} {2 m c^{2}} t \mathrm{s u n}.
$$
F. $$
-\frac{R^{2} L_{\odot}} {2 m c^{2}} t \mathrm{s u n}.
$$
G. $$
-\frac{R L_{\odot}} {2 m c^{2} R_{\odot}} t \mathrm{s u n}.
$$
H. $$
-\frac{R^{2} L_{\odot}} {m c R_{\odot}} t \mathrm{s u n}.
$$
I. $$
-\frac{R^{3} L_{\odot}} {m c^{2}} t \mathrm{s u n}.
$$
J. $$
-\frac{R} {m c^{2} R_{\odot}} t \mathrm{s u n}.
$$
Answer: F
If all of the angular momentum that is tied up in the rest of the Solar System could be returned to the Sun, what would its rotation period be (assume rigid-body rotation)? Refer to the data in Fig. 23.8. The moment-of-inertia ratio of the Sun is 0.073.

Options:
A. $$
3. 4 7 \ \mathrm{d}.
$$
B. $$
0. 1 6 \ \mathrm{d}.
$$
C. $$
4. 3 6 \ \mathrm{d}.
$$
D. $$
1. 7 9 \ \mathrm{d}.
$$
E. $$
5. 9 2 \ \mathrm{d}.
$$
F. $$
9. 4 5 \ \mathrm{d}.
$$
G. $$
6. 1 1 \ \mathrm{d}.
$$
H. $$
7. 8 3 \ \mathrm{d}.
$$
I. $$
2. 5 4 \ \mathrm{d}.
$$
J. $$
8. 0 2 \ \mathrm{d}.
$$
Answer: B
The optical signal of a specific wavelength will lose 55% of its power after spreading 3.5 km in the fiber. What is the loss of this fiber? It is expressed in dB/km.

Options:
A. $$
0. 9 6 7 \ \mathrm{d B} / \mathrm{k m}
$$
B. $$
1. 1 0 0 \ \mathrm{d B} / \mathrm{k m}
$$
C. $$
0. 9 9 1 \ \mathrm{d B} / \mathrm{k m}
$$
D. $$
0. 9 8 0 \ \mathrm{d B} / \mathrm{k m}
$$
E. $$
0. 9 7 3 \ \mathrm{d B} / \mathrm{k m}
$$
F. $$
1. 0 1 5 \ \mathrm{d B} / \mathrm{k m}
$$
G. $$
1. 0 2 3 \ \mathrm{d B} / \mathrm{k m}
$$
H. $$
1. 0 5 6 \ \mathrm{d B} / \mathrm{k m}
$$
I. $$
1. 0 0 9 \ \mathrm{d B} / \mathrm{k m}
$$
J. $$
0. 8 5 0 \ \mathrm{d B} / \mathrm{k m}
$$
Answer: C
Uniform fiber, if $n_{1}=1.5$, $\lambda_{0}=1.3$ µm, calculate: if $\Delta=0.25$, what should the core radius be to ensure single-mode transmission?

Options:
A. $$
\frac{2 \pi} {\lambda} a n_{1} \ \ \sqrt{\Delta}
$$
B. $$
\frac{\pi a} {\lambda} n_{1} \ \ \Delta \sqrt{2}
$$
C. $$
\frac{4 \pi a} {\lambda} n_{1} \ \ \sqrt{\Delta}
$$
D. $$
\frac{2 \pi a} {\lambda} n_{1} \ \ \sqrt{2 \Delta}
$$
E. $$
\frac{2 \pi a} {\Delta \lambda} n_{1} \ \ \sqrt{2}
$$
F. $$
\frac{\pi a n_{1}} {\lambda \sqrt{2 \Delta}}
$$
G. $$
\frac{\pi a} {2 \lambda} n_{1} \ \ \Delta
$$
H. $$
\frac{2 \pi a} {\lambda} \sqrt{n_{1} \Delta}
$$
I. $$
\frac{\pi a} {\lambda} n_{1} \ \ \sqrt{4 \Delta}
$$
J. $$
\frac{2 a n_{1}} {\pi \lambda} \ \ \sqrt{2 \Delta}
$$
Answer: D
A step-index optical fiber core refractive index $n_{1}= 1.4258$, cladding refractive index $n_{2}= 1.4205$, the fiber works in the $1.3\mu m$ and $1.55\mu m$ bands. What is the maximum core diameter of the fiber when it is a single mode?

Options:
A. $$
\leq5. 1 2 \ \mu\mathrm{m} \
$$
B. $$
\leq5. 0 5 \ \mu\mathrm{m} \
$$
C. $$
\leq4. 8 7 \ \mu\mathrm{m} \
$$
D. $$
\leq4. 7 5 \ \mu\mathrm{m} \
$$
E. $$
\leq4. 8 3 \ \mu\mathrm{m} \
$$
F. $$
\leq4. 9 3 \ \mu\mathrm{m} \
$$
G. $$
\leq5. 2 0 \ \mu\mathrm{m} \
$$
H. $$
\leq4. 6 8 \ \mu\mathrm{m} \
$$
I. $$
\leq4. 9 0 \ \mu\mathrm{m} \
$$
J. $$
\leq5. 1 0 \ \mu\mathrm{m} \
$$
Answer: E
Short-wavelength LEDs can be made from the material $\mathrm{Ga}...{x} \mathrm{Al}_{x} \mathrm{As}$, where $x$ represents the composition fraction. The bandgap energy of such a material is given by $E_{g}(\mathrm{eV}) = 1.424 + 1.266x + 0.266x^{2}$. It is known that $x$ must satisfy $0 \leqslant x \leqslant 0.37$. Determine the wavelength range that such an LED can cover _____.

Options:
A. $$
0. \, 5 7 0 \! \sim\! 0. \, 7 5 \, \, \mu\mathrm{m}
$$
B. $$
0. \, 6 4 8 \! \sim\! 0. \, 8 6 \, \, \mu\mathrm{m}
$$
C. $$
0. \, 5 8 5 \! \sim\! 0. \, 7 7 \, \, \mu\mathrm{m}
$$
D. $$
0. \, 6 1 0 \! \sim\! 0. \, 8 2 \, \, \mu\mathrm{m}
$$
E. $$
0. \, 6 4 3 \! \sim\! 0. \, 8 7 \, \, \mu\mathrm{m}
$$
F. $$
0. \, 6 6 2 \! \sim\! 0. \, 8 9 \, \, \mu\mathrm{m}
$$
G. $$
0. \, 6 5 0 \! \sim\! 0. \, 9 0 \, \, \mu\mathrm{m}
$$
H. $$
0. \, 6 2 0 \! \sim\! 0. \, 8 4 \, \, \mu\mathrm{m}
$$
I. $$
0. \, 7 3 0 \! \sim\! 0. \, 9 1 \, \, \mu\mathrm{m}
$$
J. $$
0. \, 5 5 4 \! \sim\! 0. \, 7 3 \, \, \mu\mathrm{m}
$$
Answer: E
The system's average transmission power is $\bar{P}_{t} = -3$ dBm, the receiver sensitivity is $\bar{P}_{\mathrm{r}} = -42$ dBm, the device margin is $M_{\mathrm{e}} = 3~\mathrm{dB}$, connector loss is $\alpha_{c} = 0.3~\mathrm{dB/pair}$, optical fiber loss coefficient is $\alpha_{\mathrm{f}} = 0.35~\mathrm{dB/km}$, optical fiber margin is $\alpha_{\mathrm{m}} = 0.1~\mathrm{dB/km}$, and the average splice loss per kilometer of optical fiber is $\alpha_{\mathrm{s}} = 0.03~\mathrm{dB/km}$.What is the relay distance?

Options:
A. $$
\approx 6 8 \mathrm{~ k m}
$$
B. $$
\approx 7 0 \mathrm{~ k m}
$$
C. $$
\approx 6 4 \mathrm{~ k m}
$$
D. $$
\approx 8 2 \mathrm{~ k m}
$$
E. $$
\approx 7 2 \mathrm{~ k m}
$$
F. $$
\approx 8 0 \mathrm{~ k m}
$$
G. $$
\approx 7 8 \mathrm{~ k m}
$$
H. $$
\approx 6 6 \mathrm{~ k m}
$$
I. $$
\approx7 4 \mathrm{~ k m}
$$
J. $$
\approx 7 6 \mathrm{~ k m}
$$
Answer: I
The step-index fiber core diameter is $2a = 50 \ \mu\mathrm{m}$, $\Delta = 0.01$, $n_{1} = 1.45$. When $\lambda = 0.8 \ \mu\mathrm{m}$, what are the normalized frequency $V$ and the number of modes that can be transmitted in the fiber?

Options:
A. 39.55, 775
B. 40.24, 810
C. 38.50, 700
D. 40.00, 755
E. 39.76, 780
F. 41.89, 850
G. 43.50, 900
H. 37.80, 710
I. 42.15, 820
J. 44.10, 880
Answer: B
There is a step-index optical fiber with a core diameter of $2a \equiv 50 \ \mu\mathrm{m}$, $n_{1} = 1.48$, $n_{2} = 1.46$, and an operating wavelength of $0.82 \ \mu\mathrm{m}$. How many modes can be transmitted in the optical fiber? When $\lambda = 1.3 \ \mu\mathrm{m}$, how many modes can be transmitted?

Options:
A. 1042;
385
B. 1125;
550
C. 1078;
429
D. 1050;
400
E. 1115;
560
F. 1090;
490
G. 1070;
430
H. 102;
500
I. 1035;
370
J. 1088;
450
Answer: C
What is the total number of bytes, total number of bits, and transmission rate of the $\mathrm{STM}-16$ frame structure?

Options:
A. 38,880 bytes, 311,040 bits, 2,488.32 Mb/s
B. 38,600 bytes, 309,000 bits, 2,450.00 Mb/s
C. 38,800 bytes, 310,400 bits, 2,480.00 Mb/s
D. 39,000 bytes, 312,000 bits, 2,500.00 Mb/s
E. 39,200 bytes, 315,200 bits, 2,460.32 Mb/s
F. 38,500 bytes, 308,000 bits, 2,460.00 Mb/s
G. 38,850 bytes, 310,900 bits, 2,485.00 Mb/s
H. 39,100 bytes, 314,100 bits, 2,505.00 Mb/s
I. 38,900 bytes, 312,500 bits, 2,490.32 Mb/s
J. 38,700 bytes, 309,600 bits, 2,470.00 Mb/s
Answer: A
It is generally assumed that the output optical power $P(t)$ of a light-emitting device decays exponentially over time, i.e.,
$P(t) = P_{0} e^{-t/\tau_{m}}$,
where $\tau_{m}$ is the degradation time constant. If, through sampling tests, it is estimated that the average time for the power attenuation of a batch of the same model light-emitting devices to drop by 3 dB at room temperature is $5 \times 10^{4} \mathrm{h}$, calculate the value of $\tau_{m}$ for this model. Furthermore, if one such device exhibits an output optical power of $1 \, \mathrm{mW}$ at room temperature, predict the output optical power of this device after 1 month, 1 year, and 5 years of use How many are they?

Options:
A. $$
5. 6 0 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 8 \mathrm{m} \mathrm{W},0.420mW,0.62mW
$$
B. $$
6. 3 0 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 7 \mathrm{m} \mathrm{W},0.400mW,0.50mW
$$
C. $$
7. 5 0 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 3 \mathrm{m} \mathrm{W},0.390mW,0.48mW
$$
D. $$
7. 8 5 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 5 \mathrm{m} \mathrm{W},0.415mW,0.47mW
$$
E. $$
6. 7 8 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 5 \mathrm{m} \mathrm{W},0.405mW,0.53mW
$$
F. $$
7. 2 1 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 9 \mathrm{m} \mathrm{W},0.389mW,0.54mW
$$
G. $$
8. 3 2 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 2 \mathrm{m} \mathrm{W},0.375mW,0.52mW
$$
H. $$
6. 9 2 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 8 \mathrm{m} \mathrm{W},0.380mW,0.55mW
$$
I. $$
8. 1 0 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 6 \mathrm{m} \mathrm{W},0.370mW,0.58mW
$$
J. $$
5. 8 7 \times1 0^{4} \mathrm{h};
$$
$$
0. 9 4 \mathrm{m} \mathrm{W},0.410mW,0.60mW
$$
Answer: F
A single-mode optical fiber has a core radius of $a = 4.5 \mu\mathrm{m}$, a core refractive index of $n_{1} = 1.47$, and a cladding refractive index of $n_{2} = 1.465$. Given $V = 2.40$, determine the mode field diameter of the fiber is().

Options:
A. $$8.9\mu m$$
B. $$7.2\mu m$$
C. $$6.8\mu m$$
D. $$8.5\mu m$$
E. $$10.8\mu m$$
F. $$11.3\mu m$$
G. $$10.2\mu m$$
H. $$9.5\mu m$$
I. $$9.9\mu m$$
J. $$12.1\mu m$$
Answer: I
It is known that the depletion region width of the Si-PIN photodiode is $40\mu m$, and the depletion region width of the InGaAs-PIN photodiode is $4{\mu\mathrm{m}}$. The drift velocity of photogenerated carriers in both is $10^{5} \mathrm{m/s}$, the junction capacitance is $1 \mathrm{pF}$, and the load resistance is $100 \Omega$. Question: What are the bandwidths of these two photodiodes?

Options:
A. $$
0. 3 2 0 0 \mathrm{G H z}
$$
$$
1.1168 \mathrm{G H z}
$$
B. $$
0. 3 2 5 0 \mathrm{G H z}
$$
$$
1.2500 \mathrm{G H z}
$$
C. $$
0. 3 1 8 3 \mathrm{G H z}
$$
$$
1.1368 \mathrm{G H z}
$$
D. $$
0. 3 1 5 0 \mathrm{G H z}
$$
$$
1.0953 \mathrm{G H z}
$$
E. $$
0. 3 1 0 0 \mathrm{G H z}
$$
$$
1.0056 \mathrm{G H z}
$$
F. $$
0. 3 6 0 0 \mathrm{G H z}
$$
$$
1.2000 \mathrm{G H z}
$$
G. $$
0. 3 4 0 0 \mathrm{G H z}
$$
$$
1.0567 \mathrm{G H z}
$$
H. $$
0. 3 1 2 5 \mathrm{G H z}
$$
$$
1.1000 \mathrm{G H z}
$$
I. $$
0. 3 0 4 8 \mathrm{G H z}
$$
$$
1.0284 \mathrm{G H z}
$$
J. $$
0. 3 2 8 0 \mathrm{G H z}
$$
$$
1.0890 \mathrm{G H z}
$$
Answer: C
In a parallel plane electrostatic field, if a certain part of the boundary line coincides with an electric field intensity line, how should the boundary condition for this segment of the boundary line be expressed?

Options:
A. $$
\vec{\nabla}\times\vec{E}=0
$$
B. $$
\varepsilon{\frac{\partial\varphi} {\partial t}}=0
$$
C. $$
\varepsilon{\frac{\partial^2\varphi} {\partial n^2}}=0
$$
D. $$
\varepsilon{\frac{\partial\varphi} {\partial\theta}}=0
$$
E. $$
\varepsilon\vec{\nabla}\cdot\vec{E}=0
$$
F. $$
\varepsilon_{r}\frac{\partial\varphi} {\partial t}=0
$$
G. $$
\vec{\nabla}\cdot\vec{E}=0
$$
H. $$
\vec{E}\cdot\vec{n}=0
$$
I. $$
\varepsilon{\frac{\partial\varphi} {\partial n}}=0
$$
J. $$
\frac{\partial\varphi} {\partial t}=0
$$
Answer: I
An infinitely long cylinder with a radius of $a$ has a surface current density of $K_{0} e_{a}$. What are the magnetic induction (magnetic flux density) and the vector potential in the surrounding space?

Options:
A. $$
B=\left\{\begin{matrix} {{\mu_{0} K r^{2} e_{a} \quad ( r > a )}} \\ {{\mu_{0} a K e_{z} \quad ( r \leq a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\frac{\mu_{0} r K e_{z}} {2}} \quad ( r > a )}}}} \\ {{{{\mu_{0} a^{2} e_{\phi} \quad ( r \leq a )}}}} \\ \end{matrix} \right.
$$
B. $$
B=\left\{\begin{matrix} {{\frac{\mu_{0} K r e_{z}} {a} \quad ( r \leq a )}} \\ {{\mu_{0} K e_{z} \quad ( r > a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\mu_{0} K a e_{a} \quad ( r \leq a )}}}} \\ {{{{\mu_{0} K r^{2} e_{a} \quad ( r > a )}}}} \\ \end{matrix} \right.
$$
C. $$
B=\left\{\begin{matrix} {{\mu_{0} K e_{\phi} \quad ( r \leq a )}} \\ {{0 \quad ( r > a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\mu_{0} K r^{2} e_{a} \quad ( r \leq a )}}}} \\ {{{{\mu_{0} K a e_{z} \quad ( r > a )}}}} \\ \end{matrix} \right.
$$
D. $$
B=\left\{\begin{matrix} {{\mu_{0} K e_{\phi} \quad ( r > a )}} \\ {{\mu_{0} r K e_{z} \quad ( r \leq a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\mu_{0} K a e_{z} \quad ( r \leq a )}}}} \\ {{{{\frac{\mu_{0} r^{2} K e_{a}} {2}} \quad ( r > a )}}}} \\ \end{matrix} \right.
$$
E. $$
B=\left\{\begin{matrix} {{\mu_{0} K r e_{\phi} \quad ( r \leq a )}} \\ {{\mu_{0} K a e_{z} \quad ( r > a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\frac{\mu_{0} K e_{a}} {2}} \quad ( r > a )}}}} \\ {{{{\mu_{0} a^{2} e_{z} \quad ( r \leq a )}}}} \\ \end{matrix} \right.
$$
F. $$
B=\left\{\begin{matrix} {{0 \quad ( r > a )}} \\ {{\mu_{0} K e_{\phi} \quad ( r \leq a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\mu_{0} K r e_{\phi} \quad ( r \leq a )}}}} \\ {{{{\mu_{0} r^{2} K e_{z} \quad ( r > a )}}}} \\ \end{matrix} \right.
$$
G. $$
B=\left\{\begin{matrix} {{\mu_{0} a^{2} K e_{z} \quad ( r > a )}} \\ {{0 \quad ( r \leq a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\mu_{0} K r e_{\phi} \quad ( r \leq a )}}}} \\ {{{{\frac{\mu_{0} a^{2} K e_{z}} {2r}} \quad ( r > a )}}}} \\ \end{matrix} \right.
$$
H. $$
B=\left\{\begin{matrix} {{0 \quad ( r \leq a )}} \\ {{\mu_{0} K e_{z} \quad ( r > a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\frac{\mu_{0} a^{2} e_{a}} {2 r}} \quad ( r \leq a )}}} \\ {{{{\frac{\mu_{0} K r e_{a}} {2}} \quad ( r > a )}}} \\ \end{matrix} \right.
$$
I. $$
B=\left\{\begin{matrix} {{\mu_{0} K e_{z} \quad( r \leq a )}} \\ {{0 \quad( r > a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\frac{\mu_{0} K r e_{a}} {2}} \ \ ( r \leq a )}}} \\ {{{{\frac{\mu_{0} K a^{2} e_{a}} {2 r}} \ ( r > a )}}} \\ \end{matrix} \right.
$$
J. $$
B=\left\{\begin{matrix} {{\mu_{0} K r e_{z} \quad ( r \leq a )}} \\ {{\mu_{0} r^{2} K e_{\phi} \quad ( r > a )}} \\ \end{matrix} \right.
$$
$$
A=\left\{\begin{matrix} {{{{\frac{\mu_{0} K a e_{z}} {r}} \quad ( r > a )}}}} \\ {{{{\frac{\mu_{0} a^{2} r e_{a}} {2}} \quad ( r \leq a )}}}} \\ \end{matrix} \right.
$$
Answer: I
The coaxial cable, with an inner conductor radius of $a$ and an outer radius of $b$, carries a current $I$. Assuming the thickness of the outer conductor is negligible, what is the magnetic field energy per unit length?

Options:
A. $$
\frac{\mu_{0} I^{2}} {4 \pi} \! \left( \frac{1} {4} \!+\! \operatorname{l n} \frac{b} {a} \right)
$$
B. $$
\frac{\mu_{0} I^{2}} {8 \pi} \! \left( \frac{1} {2} \!-\! \operatorname{l n} \frac{a} {b} \right)
$$
C. $$
\frac{\mu_{0} I^{2}} {4 \pi} \! \left( \frac{1} {3} \!+\! \operatorname{l n} \frac{a} {b} \right)
$$
D. $$
\frac{\mu_{0} I^{2}} {4 \pi} \! \left( \frac{1} {8} \!+\! \operatorname{l n} \frac{a} {b} \right)
$$
E. $$
\frac{\mu_{0} I^{2}} {10 \pi} \! \left( \frac{1} {4} \!+\! \operatorname{l n} \frac{b} {a} \right)
$$
F. $$
\frac{\mu_{0} I^{2}} {8 \pi} \! \left( \frac{1} {3} \!+\! \operatorname{l n} \frac{b} {a} \right)
$$
G. $$
\frac{\mu_{0} I^{2}} {3 \pi} \! \left( \frac{1} {4} \!+\! \operatorname{l n} \frac{a} {b} \right)
$$
H. $$
\frac{\mu_{0} I^{2}} {4 \pi} \! \left( \frac{1} {2} \!-\! \operatorname{l n} \frac{b} {a} \right)
$$
I. $$
\frac{\mu_{0} I^{2}} {6 \pi} \! \left( \frac{1} {4} \!+\! \operatorname{l n} \frac{b} {a} \right)
$$
J. $$
\frac{\mu_{0} I^{2}} {2 \pi} \! \left( \frac{1} {4} \!+\! \operatorname{l n} \frac{a} {b} \right)
$$
Answer: A
It is known that in a vacuum, there is a uniform plane wave with an electric field strength $\boldsymbol{E}=E_{x} \boldsymbol{e}_{x}+E_{y} \boldsymbol{e}_{y}$. Here, $E_{x}=100 \cos (2 \pi \times 10^{8} t - 0.21 z) \; \mathrm{V/m}$, and $E_{y}=100 \cos (2 \pi \times 10^{8} t - 0.21 z + 90^{\circ}) \; \mathrm{V/m}$. What are the instantaneous value and phasor expression for the magnetic field strength?

Options:
A. $$
\dot{H}=0. 2 0 0 e^{-0. 2 1 z} \big( \boldsymbol{e}_{x}-\mathrm{j} e_{y} \big) \, \mathrm{A / m}
$$
B. $$
\dot{H}=0. 2 5 0 e^{-0. 2 1 z} \big( \boldsymbol{e}_{y}+\mathrm{j} e_{x} \big) \, \mathrm{A / m}
$$
C. $$
\dot{H}=0. 1 8 7 e^{-0. 2 5 z} \big( \boldsymbol{e}_{y}-\mathrm{j} e_{x} \big) \, \mathrm{A / m}
$$
D. $$
\dot{H}=0. 1 8 7 e^{-0. 2 1 z} \big( \boldsymbol{e}_{y}-\mathrm{j} e_{x} \big) \, \mathrm{A / m}
$$
E. $$
\dot{H}=0. 1 8 7 e^{+0. 2 1 z} \big( \boldsymbol{e}_{y}-\mathrm{j} e_{x} \big) \, \mathrm{A / m}
$$
F. $$
\dot{H}=0. 1 8 7 e^{-0. 2 1 z} \big( \boldsymbol{e}_{x}+\mathrm{j} e_{y} \big) \, \mathrm{A / m}
$$
G. $$
\dot{H}=0. 1 8 7 e^{-0. 2 1 z} \big( \boldsymbol{e}_{y}+\mathrm{j} e_{x} \big) \, \mathrm{A / m}
$$
H. $$
\dot{H}=0. 1 8 7 e^{-0. 2 1 z} \big( \boldsymbol{e}_{x}-\mathrm{j} e_{y} \big) \, \mathrm{A / m}
$$
I. $$
\dot{H}=0. 2 1 0 e^{-0. 2 1 z} \big( \boldsymbol{e}_{y}-\mathrm{j} e_{x} \big) \, \mathrm{A / m}
$$
Answer: D
A plane electromagnetic wave with a frequency of $1 \times 10^{10}$ Hz penetrates perpendicularly along the $x$-axis into a flat layer of silver. The electrical conductivity of the silver layer is $3 \times 10^{7} \mathrm{S / m}$. What is the penetration depth?

Options:
A. $$
5. 4 1 \times1 0^{-7} {\mathrm{m}}
$$
B. $$
9. 1 9 \times1 0^{-7} {\mathrm{m}}
$$
C. $$
3. 0 6 \times1 0^{-8} {\mathrm{m}}
$$
D. $$
2. 3 4 \times1 0^{-6} {\mathrm{m}}
$$
E. $$
1. 9 7 \times1 0^{-6} {\mathrm{m}}
$$
F. $$
8. 5 2 \times1 0^{-7} {\mathrm{m}}
$$
G. $$
4. 2 9 \times1 0^{-8} {\mathrm{m}}
$$
H. $$
7. 3 5 \times1 0^{-8} {\mathrm{m}}
$$
I. $$
6. 8 1 \times1 0^{-7} {\mathrm{m}}
$$
J. $$
1. 2 8 \times1 0^{-6} {\mathrm{m}}
$$
Answer: B
The complex vector of a certain electromagnetic field is given as:
$$
\begin{array} {c}
\boldsymbol{E}(z) = e_x j E_0 \sin(k_0 z) \quad \mathrm{V/m} \\
\boldsymbol{H}(z) = e_y \sqrt{\frac{E_0}{\mu_0}} E_0 \cos(k_0 z) \quad \mathrm{A/m} \\
\end{array}
$$
where $k_0 = \frac{2\pi}{\lambda_0} = \frac{\omega}{c}$, $c$ is the speed of light in a vacuum, and $\lambda_0$ is the wavelength.
Find:
The instantaneous Poynting vector at points $z = 0$, $\frac{\lambda_0}{8}$, and $\frac{\lambda_0}{4}$ is().

Options:
A. $$
= E_0 \quad{\bf W} / {\bf m}^{2}
$$
B. $$
= \frac{\omega E_0}{c} \quad{\bf W} / {\bf m}^{2}
$$
C. $$
= 1.5 \mu_0 E_0 \quad{\bf W} / {\bf m}^{2}
$$
D. $$
= -\frac{\pi E_0}{\lambda_0} \quad{\bf W} / {\bf m}^{2}
$$
E. $$
= k_0 \lambda_0 \quad{\bf W} / {\bf m}^{2}
$$
F. $$
= \sqrt{2} \quad{\bf W} / {\bf m}^{2}
$$
G. $$
= \frac{E_0^2}{2\mu_0} \quad{\bf W} / {\bf m}^{2}
$$
H. $$
= -\mu_0 \quad{\bf W} / {\bf m}^{2}
$$
I. $$
= \sin^2(k_0 z) E_0 \quad{\bf W} / {\bf m}^{2}
$$
J. $$
= 0 \quad{\bf W} / {\bf m}^{2}
$$
Answer: J
In a non-magnetic medium with a relative permittivity $\mathcal{E} _{r}=2.5$ and a loss tangent of $10^{-2}$, a uniform plane wave with a frequency of $3 \ \mathrm{GHz}$, polarized in the $\boldsymbol{e}$ direction, propagates in the $e$ direction. Assume that at $x=0$:
$$E(0,~t) = e_{y}~50~\sin(6 \pi \times 10^{9}t + \frac{\pi}3).$$
Write the expression for $H(x, t)$ is ().

Options:
A. $$
e_{z} 0. \, 2 1 {\mathrm{e}}^{-0.497 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi \times 10^9 t \,-\, 3 1. \, 6 \, \pi \, x \,+\, {\frac{\pi} {4}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
B. $$
e_{z} 0. \, 2 2 \, {\mathrm{e}}^{-0.497 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times1 0^{9} t \,-\, 3 1. \, 6 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 5 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
C. $$
e_{z} 0. \, 2 0 \, {\mathrm{e}}^{-0.497 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times 1 0^{8} t \,-\, 3 1. \, 6 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
D. $$
e_{z} 0. \, 2 1 \, {\mathrm{e}}^{-0.498 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times 1 0^{9} t \,-\, 3 1. \, 6 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
E. $$
e_{z} 0. \, 2 1 \, {\mathrm{e}}^{-0.496 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times1 0^{9} t \,-\, 3 1. \, 7 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
F. $$
e_{z} 0. \, 2 3 \, {\mathrm{e}}^{-0.497 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi \, \times10^{9} t \,-\, 3 2. \, 6 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
G. $$
e_{z} 0.1 9 \, {\mathrm{e}}^{-0.497 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times1 0^{9} t \,-\, 3 1.5 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 7 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
H. $$
e_{z} 0. \, 2 1 \, {\mathrm{e}}^{-0.497 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times1 0^{\circ} t \,-\, 3 1. \, 6 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
I. $$
e_{z} 0. \, 2 2 \, {\mathrm{e}}^{-0.495 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times 9 t \,-\, 3 1. \, 6 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
J. $$
e_{z} 0.15 \, {\mathrm{e}}^{-0.497 \, {\mathrm{x}}} \operatorname{s i n} {\Bigl(} 6 \, \pi\times1 0^{9} t \,-\, 3 1. \, 6 \, \pi x \,+\, {\frac{\pi} {3}} \,-\, 0. \, 0 0 1 \, 6 \, \pi{\Bigr)} \quad{\mathrm{A / m}}
$$
Answer: H
A uniform plane wave is incident from medium 1 onto the planar boundary with medium 2. Given that $\sigma_{1}=\sigma_{2}= 0$, $\mu_{1}=\mu_{2}=\mu_{0}$, determine the value of $\frac{\varepsilon_{r2}}{\varepsilon_{r1}}$ when 10% of the average power of the incident wave is reflected is().

Options:
A. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=4.01 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.249
$$
B. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=3.00 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.333
$$
C. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=2.45 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.408
$$
D. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=6.12 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.163
$$
E. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=3.68 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.269
$$
F. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=2.71 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.369
$$
G. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=4.67 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.214
$$
H. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=1.89 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.530
$$
I. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=5.89 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.170
$$
J. $$
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=5.23 \text{ or }
\frac{\varepsilon_{r 1}} {\varepsilon_{r 2}}=0.191
$$
Answer: E
In free space $(z < 0)$, a uniform plane wave propagates in the $+z$ direction and is incident perpendicularly on a conductive plane at $z = 0$. The conductivity of the conductor is $\sigma = 61.7 \, \mathrm{MS/m}$, and the relative permeability is $\mu_r = 1$. The frequency of the electromagnetic wave in free space is $f = 1.5 \, \mathrm{MHz}$, and the amplitude of the electric field is 1 V/m. At the interface $(z = 0)$, $E$ is given by the following equation:
$$
E(0, t) = e_y \sin 2 \pi f t
$$
For the region $z > 0$, find $H_2(z, t)$ is ().

Options:
A. $$
\begin{array} {c} {{{{=-\, e_{z} 0. \, 8 7 \, \times\, 1 0^{-3} \, e^{-1. 5 5 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 2 \, \pi\times\, 1 0^{6} \, t \,-\, 1. \, 8 9 \, \times\, 1 0^{5} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
B. $$
\begin{array} {c} {{{{=-\, e_{x} 0. \, 5 3 \, \times\, 1 0^{-4} \, e^{-1. 7 7 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 2 \, \pi\times\, 1 0^{7} \, t \,-\, 1. \, 2 0 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
C. $$
\begin{array} {c} {{{{=-\, e_{x} 0. \, 3 1 \, \times\, 1 0^{-2} \, e^{-2. 1 4 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 1 \, \pi\times\, 1 0^{5} \, t \,-\, 3. \, 1 7 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
D. $$
\begin{array} {c} {{{{=-\, e_{y} 0. \, 7 2 \, \times\, 1 0^{-2} \, e^{-1. 8 9 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 4 \, \pi\times\, 1 0^{6} \, t \,-\, 2. \, 0 3 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
E. $$
\begin{array} {c} {{{{=-\, e_{y} 1. \, 4 0 \, \times\, 1 0^{-3} \, e^{-1. 2 7 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 6 \, \pi\times\, 1 0^{5} \, t \,-\, 2. \, 0 5 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
F. $$
\begin{array} {c} {{{{=-\, e_{x} 0. \, 9 5 \, \times\, 1 0^{-5} \, e^{-1. 4 6 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 7 \, \pi\times\, 1 0^{5} \, t \,-\, 1. \, 9 2 \, \times\, 1 0^{3} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
G. $$
\begin{array} {c} {{{{=-\, e_{y} 1. \, 0 3 \, \times\, 1 0^{-2} \, e^{-1. 9 4 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 3 \, \pi\times\, 1 0^{8} \, t \,-\, 1. \, 3 1 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
H. $$
\begin{array} {c} {{{{=-\, e_{z} 0. \, 4 5 \, \times\, 1 0^{-3} \, e^{-2. 2 1 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 2 \, \pi\times\, 1 0^{5} \, t \,-\, 2. \, 2 1 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
I. $$
\begin{array} {c} {{{{=-\, e_{x} 0. \, 5 3 \, \times\, 1 0^{-2} \, e^{-1. 9 1 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 3 \, \pi\times\, 1 0^{6} \, t \,-\, 1. \, 9 1 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
J. $$
\begin{array} {c} {{{{=-\, e_{z} 2. \, 5 7 \, \times\, 1 0^{-3} \, e^{-1. 6 8 \times1 0^{4} z}}}}} \\ {{{{\operatorname{s i n} \left( \, 5 \, \pi\times\, 1 0^{5} \, t \,-\, 2. \, 4 6 \, \times\, 1 0^{4} z \right) \quad\mathrm{A / m}}}}} \\ \end{array}
$$
Answer: I
Design a rectangular waveguide operating at a wavelength of $\lambda = 10$ cm, made of copper and filled with air. It is required that the operating frequency of the $\mathbf{TE}_{10}$ mode has at least a 30% safety margin, i.e., $0.7 f_{c2} \geq f \geq 1.3 f_{c1}$, where $f_{c1}$ and $f_{c2}$ represent the cutoff frequencies of the $\mathrm{TE}_{10}$ mode and the adjacent higher-order mode, respectively is ().

Options:
A. $$
= 6. 7 \ \mathrm{c m} \times3. 5 \ \mathrm{c m}
$$
B. $$
= 7. 4 \ \mathrm{c m} \times3. 7 \ \mathrm{c m}
$$
C. $$
= 7. 3 \ \mathrm{c m} \times3. 6 \ \mathrm{c m}
$$
D. $$
= 6. 6 \ \mathrm{c m} \times3. 3 \ \mathrm{c m}
$$
E. $$
= 7. 2 \ \mathrm{c m} \times3. 6 \ \mathrm{c m}
$$
F. $$
= 6. 8 \ \mathrm{c m} \times3. 4 \ \mathrm{c m}
$$
G. $$
= 7. 1 \ \mathrm{c m} \times3. 6 \ \mathrm{c m}
$$
H. $$
= 6. 9 \ \mathrm{c m} \times3. 4 \ \mathrm{c m}
$$
I. $$
= 6. 5 \ \mathrm{c m} \times3. 2 \ \mathrm{c m}
$$
J. $$
= 7. 0 \ \mathrm{c m} \times3. 5 \ \mathrm{c m}
$$
Answer: F
Consider a lossless transmission line. When the load impedance is $Z_{\mathrm{L}} = (40 - \mathrm{j} 30) \, \Omega$, what should the characteristic impedance of the line be in order to minimize the standing wave ratio?

Options:
A. $$
= 4 0 \; \; \Omega
$$
B. $$
= 6 0 \; \; \Omega
$$
C. $$
= 3 5 \; \; \Omega
$$
D. $$
= 5 0 \; \; \Omega
$$
E. $$
= 5 5 \; \; \Omega
$$
F. $$
= 1 0 0 \; \; \Omega
$$
G. $$
= 8 0 \; \; \Omega
$$
H. $$
= 9 0 \; \; \Omega
$$
I. $$
= 2 5 \; \; \Omega
$$
J. $$
= 7 0 \; \; \Omega
$$
Answer: D
To achieve an effective value of the electric field strength greater than $100 \, \mu\mathrm{V / m}$ at a distance of 100 km in the direction perpendicular to the axis of a Hertzian dipole, how much power must the Hertzian dipole radiate at a minimum?

Options:
A. $$
4. 4 6 \mathrm{~ W}
$$
B. $$
5. 5 5 \mathrm{~ W}
$$
C. $$
1. 1 1 \mathrm{~ W}
$$
D. $$
2. 2 2 \mathrm{~ W}
$$
E. $$
8. 0 1 \mathrm{~ W}
$$
F. $$
9. 9 0 \mathrm{~ W}
$$
G. $$
7. 7 7 \mathrm{~ W}
$$
H. $$
3. 3 3 \mathrm{~ W}
$$
I. $$
6. 0 0 \mathrm{~ W}
$$
J. $$
0. 9 8 \mathrm{~ W}
$$
Answer: D
Experimental results show that the homogeneous decomposition reaction of nitrous oxide is:
$$
\mathrm{N_{2} O} \longrightarrow \mathrm{N_{2}} + \frac{1}{2} \mathrm{O_{2}}
$$
The rate expression is given as:
$$
(-r_{\mathrm{N_{2} O}}) \!=\! \frac{k_{1} [ c_{\mathrm{N_{2} O}} ]^{2}}{1 \!+\! k_{2} [ c_{\mathrm{N_{2} O}} ]} \, \mathrm{mol / (L \cdot min)}
$$
Where
$$
k_{1} \!=\! 10^{19.39} \mathrm{e}^{-342251}/ (R T) \, ;
$$
$$
k_{2} \!=\! 10^{8.69} \mathrm{e}^{-118826}/ (R T) \,.
$$
What is the activation energy of the reaction at high temperature and high concentration?

Options:
A. $$
2 2 3 4 2 5 \ \mathrm{J / m o l}
$$
B. $$
2 4 6 8 1 0 \ \mathrm{J / m o l}
$$
C. $$
1 0 9 8 7 6 \ \mathrm{J / m o l}
$$
D. $$
1 1 1 1 1 1 \ \mathrm{J / m o l}
$$
E. $$
1 2 3 4 5 6 \ \mathrm{J / m o l}
$$
F. $$
3 4 5 6 7 8 \ \mathrm{J / m o l}
$$
G. $$
2 7 8 3 1 9 \ \mathrm{J / m o l}
$$
H. $$
3 3 3 4 4 4 \ \mathrm{J / m o l}
$$
I. $$
9 8 7 6 5 4 \ \mathrm{J / m o l}
$$
J. $$
2 5 6 1 7 8 \ \mathrm{J / m o l}
$$
Answer: A