Electricity and Magnetism
Core concepts
Electrostatics: Coulomb's law, electric field E = F/q, Gauss's law (flux = Q_enc/ε₀), and potential V with E = −dV/dx. Capacitance C = Q/V, energy ½CV², and dielectrics multiplying C by κ. Circuits: Ohm's law, series and parallel resistor rules, Kirchhoff's laws, and RC time constant τ = RC. Magnetism: force on a moving charge F = qv×B, force on a wire F = BIL sinθ, and Ampère's law for fields from currents. Induction: Faraday's law ε = −dΦ/dt, Lenz's law opposing change, and motional emf ε = Bℓv. Maxwell's equations unify the fields and predict electromagnetic waves at speed c = 1/√(μ₀ε₀).
Traps
Lenz's law questions test direction, not magnitude-determine the change in flux first. Magnetic forces do no work on charges. In circuits, ammeters go in series and voltmeters in parallel; ideal versions have zero and infinite resistance respectively. RC charging versus discharging have different initial conditions. Superposition of fields is vector addition, so direction errors are frequent.
Worked example
A 12 V battery drives a 4 Ω and 6 Ω resistor in series: R_total = 10 Ω, current = 1.2 A, and power dissipated in the 4 Ω resistor is I²R = 5.76 W. Rule of thumb: in series, current is shared and voltage divides; in parallel, voltage is shared and current divides.