Electricity and Magnetism
Core concepts
Master Coulomb's law, electric field and potential, Gauss's law and symmetry, capacitance and energy storage, DC circuits (Kirchhoff's rules, series/parallel), magnetic force on moving charges and currents, Ampère's law, Faraday's law of induction, and Maxwell's equations in integral form. Understand that electric potential is a scalar and superposition is easier with it than with fields.
Traps
- Field vs. potential: E = −∇V; a region of constant potential has zero field, and zero potential does not imply zero field.
- Gauss's law gives easy answers only with high symmetry (sphere, cylinder, infinite plane).
- Sign of induced EMF: Lenz's law opposes the change in flux, not the flux itself.
- Circuits: voltage is shared in series, current in parallel; internal resistance changes terminal voltage.
- Magnetic force does no work on a charge because F ⊥ v.
Worked example
Two resistors, 6 Ω and 3 Ω, in parallel across 12 V. Each branch sees 12 V, so currents are 2 A and 4 A, total 6 A, equivalent resistance 2 Ω. Trap: students often add resistances in parallel as 6 + 3 = 9 Ω. Check with the reciprocal rule: 1/R = 1/6 + 1/3 = 1/2, R = 2 Ω.
Rule of thumb
Use potential (scalar) wherever possible, and reserve vector field calculations for cases where direction matters or symmetry is high.