Electricity, Magnetism, and Waves
What the exam tests
Electrostatics, direct-current circuits, capacitors, magnetic forces and induction, and basic wave behaviour. Questions are usually quantitative and test whether you can combine a circuit rule with an energy or field calculation.
Core rules
- Coulomb's law: F=k|q₁q₂|/r², with k≈9×10⁹ N·m²/C². Electric field E=F/q; a uniform field between plates has E=V/d.
- Ohm's law: V=IR. In series the current is the same and R_eq=ΣR; in parallel the voltage is the same and 1/R_eq=Σ1/R.
- Kirchhoff: the junction rule expresses charge conservation; the loop rule expresses energy conservation. A real cell has terminal voltage V=ε−Ir.
- Capacitors: Q=CV, energy ½CV². Capacitors in parallel add; in series the reciprocals add.
- Magnetic force: F=qvB sinθ on a moving charge, F=BIL sinθ on a current-carrying wire. Faraday's law: ε=−dΦ/dt; Lenz's law gives the direction.
- Waves: v=fλ; for a sinusoidal supply, V_rms=V_peak/√2 and I_rms=I_peak/√2.
Worked example
A cell of EMF 12 V and internal resistance 1 Ω is connected to a 5 Ω resistor. Total resistance = 1+5=6 Ω, so I=ε/(R+r)=12/6=2 A. Terminal voltage V=ε−Ir=12−2(1)=10 V, which also equals IR=2×5. Power in the external resistor: P=I²R=4×5=20 W. Power wasted internally is I²r=4 W, so the cell delivers 24 W chemically.
Traps
- Adding internal resistance in parallel with the external resistor.
- Using peak voltage in a power calculation instead of RMS.
- Forgetting that a capacitor blocks steady direct current but not alternating current.
- Omitting sinθ when the field and velocity are not perpendicular.
- Getting the sign of an induced EMF wrong by ignoring Lenz's law.