13 Jun 2026

Electromagnetic Theory Standard Problems

Standard competitive exam problems in electromagnetic theory with answer key.

electromagnetic-theory gate-2024 csir-net-2023 jest-2022

These are original standard problems based on frequently tested competitive-exam patterns.

Q: In electrostatics, Gauss's law in differential form is
A: $\nabla\cdot\mathbf E=\rho/\epsilon_0$
B: $\nabla\times\mathbf E=\rho/\epsilon_0$
C: $\nabla\cdot\mathbf B=\rho/\epsilon_0$
D: $\nabla\times\mathbf B=0$
ANSWER: A
SOURCE: GATE 2024 style
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Q: The magnetic field inside a long solenoid with turn density $n$ carrying current $I$ is approximately
A: $\mu_0 nI$
B: $nI/\mu_0$
C: $\mu_0 I/(2\pi r)$
D: zero
ANSWER: A
SOURCE: CSIR-NET 2023 style
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Q: The Poynting vector is
A: $\mathbf E\times\mathbf B/\mu_0$
B: $\mathbf E\cdot\mathbf B$
C: $\rho\mathbf E$
D: $\nabla\cdot\mathbf E$
ANSWER: A
SOURCE: JEST 2022 style
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Q: In vacuum, the speed of electromagnetic waves is
A: $\sqrt{\mu_0\epsilon_0}$
B: $1/\sqrt{\mu_0\epsilon_0}$
C: $\mu_0/\epsilon_0$
D: $\epsilon_0/\mu_0$
ANSWER: B
SOURCE: GATE 2021 style
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Q: For a perfect conductor in electrostatic equilibrium, the electric field inside is
A: infinite
B: uniform but nonzero
C: zero
D: parallel to current density
ANSWER: C
SOURCE: CSIR-NET 2020 style
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Q: The capacitance of an isolated parallel-plate capacitor of area $A$ and separation $d$ is
A: $\epsilon_0 A/d$
B: $\epsilon_0 d/A$
C: $A/(\epsilon_0 d)$
D: $d/(\epsilon_0 A)$
ANSWER: A
SOURCE: GATE style
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Q: The boundary condition for the normal component of $\mathbf B$ across an interface is
A: discontinuous by $\sigma/\epsilon_0$
B: continuous
C: always zero
D: infinite
ANSWER: B
SOURCE: CSIR-NET style
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Q: In Coulomb gauge, the vector potential satisfies
A: $\nabla\cdot\mathbf A=0$
B: $\nabla\times\mathbf A=0$
C: $\mathbf A=0$
D: $\partial\mathbf A/\partial t=0$
ANSWER: A
SOURCE: JEST style

Problem Sheet Standard MCQs