Electricity and Magnetism
This domain draws on electrostatics, direct-current circuits, magnetism, and electromagnetic induction. The exam favors multi-step circuit problems and qualitative reasoning about fields and induced currents.
Core rules
- Coulomb's law. F = kq₁q₂/r² with k ≈ 9.0 × 10⁹ N·m²/C². Force acts along the line joining the charges; like charges repel.
- Field and potential. E = kq/r² is a vector; V = kq/r is a scalar, so potentials add algebraically while fields add as vectors.
- Circuits. V = IR for ohmic devices. Series: R_eq = ΣR, shared current. Parallel: 1/R_eq = Σ1/R, shared voltage.
- Magnetism. F = qvB sin θ and F = BIL sin θ; direction from the right-hand rule.
- Induction. ε = −N ΔΦ/Δt (Faraday), with Lenz's law fixing the direction so the induced current opposes the change in flux.
Worked example
A 12 V battery drives a 3.0 Ω resistor in series with a parallel pair of 4.0 Ω and 6.0 Ω. For the pair, 1/R = 1/4 + 1/6 = 5/12, so R = 2.4 Ω. Total resistance = 5.4 Ω, giving I = 12/5.4 = 2.2 A. The parallel pair drops V = 2.2 × 2.4 = 5.3 V, so the 4 Ω branch carries 1.33 A and the 6 Ω branch 0.89 A, summing to the 2.2 A total.
Traps
- Treating current as "used up" around a circuit; charge is conserved.
- Adding parallel resistances as though they were in series.
- Believing the magnetic force changes a charge's speed - it is always perpendicular to v and does no work.
- Reversing Lenz's law: rising flux and falling flux give opposite induced current directions.