Electricity and Magnetism
Core concepts
Electrostatics: Coulomb's law, electric field, potential, Gauss's law for symmetric charge distributions, capacitance (C = Q/V, energy ½CV²). DC circuits: Ohm's law, Kirchhoff's rules, series/parallel combinations, internal resistance, power dissipation. AC circuits: rms values, reactance of capacitors and inductors, impedance, resonance at ω = 1/√(LC). Magnetism: force on moving charge (F = qv × B), force on a current-carrying wire, field of a long straight wire and a solenoid. Electromagnetic induction: Faraday's law, Lenz's law (direction of induced current opposes change in flux), motional emf.
Traps
- Confusing potential (scalar) with field (vector).
- Forgetting internal resistance in real batteries.
- Sign of induced emf - Lenz's law is about opposing change, not opposing flux.
- Using peak rather than rms values in AC power.
- Ignoring direction of B when computing forces.
Worked example
A rod of length L moves at speed v perpendicular to a uniform field B. Motional emf ε = BLv. If it slides on rails of resistance R, current I = BLv/R and the retarding force is F = BIL = B²L²v/R. Rule of thumb: every motional-emf problem ends with a force opposing the motion.