Electricity and Magnetism
Electricity and Magnetism covers electrostatics, current electricity, capacitance, magnetic forces and electromagnetic induction. The exam favours circuit problems with internal resistance, network reasoning with Kirchhoff's laws, and force-on-conductor or induction items set in a magnetic field.
Core rules
- Coulomb's law F = kQ₁Q₂/r² with k ≈ 9 × 10⁹ N m² C⁻²; field strength E = F/q; potential V = W/q; in a uniform field E = V/d.
- Ohm's law V = IR is obeyed only by ohmic conductors at constant temperature; a filament lamp's resistance rises as it heats.
- Resistivity: R = ρL/A, so resistance rises with length and falls with cross-sectional area.
- Series: the current is common and resistances add. Parallel: the p.d. is common and 1/R = 1/R₁ + 1/R₂ + …
- A real cell obeys E = I(R + r); the terminal p.d. is V = E − Ir and falls as current rises.
- Power: P = VI = I²R = V²/R. Kirchhoff's junction rule expresses charge conservation, the loop rule energy conservation.
- Capacitance C = Q/V; parallel capacitors add, series add reciprocally; stored energy = ½QV.
- Magnetic force F = BIL sinθ on a current and F = qvB on a moving charge; the force is zero when the conductor or velocity is parallel to the field. Fleming's left-hand rule gives the direction.
- Faraday's law: induced emf = −rate of change of flux linkage; Lenz's law states the induced current opposes the change producing it. For an ideal transformer Vs/Vp = Ns/Np, with power conserved.
Worked example
A cell of emf 12 V and internal resistance 0.5 Ω is connected to a 5.5 Ω resistor. Find the current, terminal p.d. and power in the external resistor. Total resistance = 0.5 + 5.5 = 6.0 Ω; I = 12/6.0 = 2.0 A. Terminal p.d. = E − Ir = 12 − (2.0 × 0.5) = 11 V; check with V = IR = 2.0 × 5.5 = 11 V. Power in the resistor = I²R = 4.0 × 5.5 = 22 W; total power from the cell is 12 × 2.0 = 24 W, the missing 2 W being dissipated inside the cell.
Traps that cost marks
- Quoting the emf as the terminal p.d. when current is flowing.
- Adding parallel resistances directly instead of adding reciprocals.
- Applying V = IR to a non-ohmic component from a single data point.
- Forgetting sinθ and claiming maximum force on a wire lying along the field.
- Reversing Lenz's law so that the induced current is said to aid the change.
- Assuming a transformer changes frequency or can step up power.