How much net electric flux exits a closed surface containing 8.85 nC, if ε0≈8.85×10⁻¹² F/m?
A 1 N·m²/C
B 10 N·m²/C
C 1000 N·m²/C
D 100 N·m²/C
Answer: C. 1000 N·m²/C. Gauss’s law gives Q/ε0 = 8.85×10⁻⁹ / 8.85×10⁻¹² = 1000 N·m²/C.
For an infinitely long uniformly charged line, doubling radial distance changes E by what factor?
A One quarter
B Two
C Four
D One half
Answer: D. One half. The field of an ideal infinite line varies as 1/r.
What is the distance dependence of E near an ideal infinite uniformly charged sheet?
A Proportional to 1/r
B Proportional to 1/r²
C Independent of distance
D Proportional to r
Answer: C. Independent of distance. Gauss’s law gives constant magnitude σ/(2ε0) on either side of an isolated sheet.
Filling a parallel-plate capacitor completely with εr=2 dielectric changes C by what factor?
A One half
B Two
C Four
D No change
Answer: B. Two. C=εA/d, so doubling permittivity doubles capacitance.
With zero potential at infinity, doubling distance from a point charge changes its V how?
A It quarters
B It doubles
C It stays fixed
D It halves
Answer: D. It halves. Point-charge potential is proportional to 1/r.
If V(x)=10−2x volts with x in metres, what is Ex?
A −2 V/m
B +10 V/m
C +2 V/m
D Zero
Answer: C. +2 V/m. Ex = −dV/dx = +2 V/m.
Which differential equation is Gauss’s electric law in matter?
A ∇×D = ρv
B ∇·D = ρv
C ∇·B = ρv
D ∇×E = ρv
Answer: B. ∇·D = ρv. The divergence of electric displacement equals free volume-charge density.
In electrostatics, what is the curl of E?
A Charge density
B Zero
C Magnetic flux
D Current density
Answer: B. Zero. Without time-varying magnetic flux, Faraday’s law gives ∇×E=0.
What does Maxwell’s equation ∇·B=0 rule out?
A Magnetic field lines
B Magnetic monopole sources
C Electromagnetic waves
D Material permeability
Answer: B. Magnetic monopole sources. Magnetic flux has no isolated beginning or end in classical electromagnetism.
A long wire carries 10 A. At r=0.1 m in vacuum, what is B approximately?
A 2 μT
B 200 μT
C 2 mT
D 20 μT
Answer: D. 20 μT. B=μ0I/(2πr)≈2×10⁻⁵ T = 20 μT.
For an air-core long solenoid, n=1000 turns/m and I=2 A. Estimate B.
A 0.251 mT
B 1.26 mT
C 25.1 mT
D 2.51 mT
Answer: D. 2.51 mT. B≈μ0nI≈(4π×10⁻⁷)(1000)(2)=2.51 mT.
A 0.4 T field crosses 0.5 m² at 60° to the surface normal. Find flux.
A 0.1 Wb
B 0.2 Wb
C 0.4 Wb
D 0.8 Wb
Answer: A. 0.1 Wb. Φ=BAcos60°=0.4×0.5×0.5=0.1 Wb.
A 50-turn coil has flux per turn changing by 0.02 Wb in 0.1 s. Average emf magnitude?
A 1 V
B 10 V
C 20 V
D 100 V
Answer: B. 10 V. |emf|=N|ΔΦ|/Δt=50×0.02/0.1=10 V.
Two long parallel wires carry currents in the same direction. What is their force?
A Repulsive
B Always zero
C Attractive
D Perpendicular to wires
Answer: C. Attractive. Parallel currents in the same direction attract.
A positive charge moves along +x through B along +z. Magnetic force points where?
A +x
B +y
C −y
D −z
Answer: C. −y. The right-hand cross product x×z points in the negative y direction.
During ideal capacitor charging, displacement current between plates equals what in the leads?
A Conduction current
B Leakage resistance
C Static surface charge
D Magnetic flux
Answer: A. Conduction current. Ampère–Maxwell law keeps current continuity through the capacitor gap.
Faraday’s integral law gives ∮E·dl equal to what?
A +dΦB/dt
B −dΦB/dt
C Enclosed charge
D Zero always
Answer: B. −dΦB/dt. The circulation of E equals the negative rate of linked magnetic-flux change.
In a material with conductivity 2 S/m and E=3 V/m, what is J?
A 1.5 A/m²
B 3 A/m²
C 9 A/m²
D 6 A/m²
Answer: D. 6 A/m². Ohmic current density is J=σE=2×3=6 A/m².
For a linear dielectric, electric energy density is which expression?
A ½εE²
B ε/E²
C ½μH²
D E²/ε
Answer: A. ½εE². The energy stored per unit volume in its electric field is ½εE².
For a linear magnetic medium, magnetic energy density in terms of B is what?
A B²/(2μ)
B μ/B²
C ½εE²
D 2μB²
Answer: A. B²/(2μ). Magnetic field energy per unit volume is B²/(2μ).
Far from a small static electric dipole, the field magnitude falls approximately as what?
A 1/r
B 1/r²
C 1/r⁴
D 1/r³
Answer: D. 1/r³. The leading far-field term of an electrostatic dipole varies as 1/r³.
What is the intrinsic impedance of free space approximately?
A 377 Ω
B 50 Ω
C 120 Ω
D 1000 Ω
Answer: A. 377 Ω. The ratio of plane-wave E to H in vacuum is about 377 ohms.
A 150 MHz plane wave travels in vacuum. What is its wavelength?
A 2 m
B 0.5 m
C 1 m
D 4 m
Answer: A. 2 m. λ=c/f≈3×10⁸/(150×10⁶)=2 m.
A lossless nonmagnetic medium has εr=4. Wave speed compared with vacuum is what?
A One quarter
B Double
C Half
D Unchanged
Answer: C. Half. v=c/√εr=c/2 when μr=1.
At higher frequency in a good conductor, skin effect generally does what?
A Raises AC resistance
B Eliminates current
C Reduces permeability to zero
D Raises DC resistance
Answer: A. Raises AC resistance. Current crowds toward the surface, reducing effective conducting area for AC.