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GRE Physics Subject Test study materials
GRE Physics Subject Test study resources

GRE Physics Subject Test: Electromagnetism

GRE Physics Subject Test · Work through your exam, one topic at a time.

All guide sections

Electromagnetism

Electromagnetism is the second-largest block of the GRE Physics Subject Test. It spans Coulomb's law and superposition, Gauss's law in integral form, potential and potential energy, capacitance and dielectrics, steady-current circuits including RC transients, magnetic fields of currents (Biot–Savart, Ampère's law), forces on moving charges, Faraday and Lenz induction, and Maxwell's equations as a synthesis.

Core rules

  • Gauss's law: flux = Q_enc/ε₀. Exploit symmetry - spherical for point charges, shells and balls; cylindrical for line charges and long solenoids; planar for sheets.
  • Potential is a scalar; V = kQ/r outside a sphere and E = −∇V. Inside a conductor in electrostatics E = 0, so the entire conductor is an equipotential.
  • Capacitors: C = ε₀A/d for a parallel plate, U = ½CV², energy density ½ε₀E². A dielectric of constant κ multiplies C by κ and reduces E by κ.
  • Circuits: RC charging V(t) = ε(1 − e^{−t/RC}), discharge decays with τ = RC. Use Kirchhoff's loop and junction rules for networks.
  • Magnetic force F = qv × B does no work; circular radius r = mv/(qB) and cyclotron frequency ω = qB/m.
  • Ampère: ∮B·dl = μ₀I_enc. Long solenoid B = μ₀nI; long straight wire B = μ₀I/2πr.
  • Faraday: emf = −dΦ_B/dt; Lenz's law gives the direction that opposes the change in flux.

Worked example

An electron is accelerated from rest through 100 V and enters a 0.010 T field perpendicular to its velocity. Find the orbital radius. First v = √(2eV/m) = √(2 × 1.6×10⁻¹⁹ × 100 / 9.11×10⁻³¹) ≈ 5.9×10⁶ m/s. Then r = mv/(eB) = (9.11×10⁻³¹ × 5.9×10⁶)/(1.6×10⁻¹⁹ × 0.010) ≈ 3.4×10⁻³ m, about 3.4 mm.

Traps

Assigning a nonzero electrostatic field inside a conductor; increasing E instead of reducing it when a dielectric is inserted; Lenz's-law sign errors when flux is decreasing rather than increasing; using total current instead of enclosed current in Ampère's law; mixing up series and parallel rules for capacitors, which are opposite to resistors; treating the RC time constant as the time to charge completely rather than to 63%.