Electricity and Magnetism
Electricity and Magnetism: what is tested
This domain examines Coulomb's law, electric field and potential, capacitance, DC circuits, magnetic forces and fields, and electromagnetic induction. The exam favours multi-step circuits and direction questions, so track both magnitude and sign.
Core rules
- Coulomb force F = kQq/r²; electric field E = F/q = kQ/r². Field is a vector; potential V = kQ/r is a scalar. In one dimension E = −dV/dx.
- For parallel plates, the field magnitude is E = V/d. Capacitance C = Q/V; for parallel plates C = ε₀A/d. Energy stored is ½CV².
- Series: same current, voltages add, R_eq = ΣR. Parallel: same voltage, currents add, 1/R_eq = Σ1/R.
- Kirchhoff's rules: the junction rule expresses charge conservation; the loop rule expresses energy conservation. Include internal resistance and consistent sign conventions.
- Magnetic force on a moving charge is F = qvB sinθ, with direction from Fleming's left-hand rule; on a wire F = BIL sinθ. The magnetic force on a moving charge is perpendicular to velocity and does no work.
- Faraday's law: emf = −N dΦ/dt, where Φ = BA cosθ. Lenz's law gives the direction: the induced current opposes the change in flux.
Worked example
A 12 V supply with negligible internal resistance connects a 4.0 Ω resistor in series with a parallel pair of 6.0 Ω and 3.0 Ω. The parallel equivalent is (6 × 3)/(6 + 3) = 2.0 Ω, so total resistance is 6.0 Ω and supply current I = 12/6.0 = 2.0 A. The parallel voltage is IR = 2.0 × 2.0 = 4.0 V. Branch currents are 4.0/6.0 = 0.67 A and 4.0/3.0 = 1.33 A; they sum to 2.0 A.
Traps that cost marks
Do not confuse field and potential: zero field does not imply zero potential. In circuits, conventional current leaves the positive terminal externally, while electron flow is opposite. For induced emf, ask what changes-B, area, or angle-not merely what the flux is. A conductor moving parallel to a magnetic field has no induced emf. Reverse the magnetic-force direction for a negative charge.