Magnetism and Electromagnetic Induction
Scope of the domain
This domain covers magnetic fields and forces on currents and moving charges, magnetic flux, electromagnetic induction, and transformers. The exam asks you to apply F = BIL and F = qvB with directions, use Faraday's and Lenz's laws, and calculate induced EMFs and transformer quantities.
Core rules
- Magnetic flux density B is measured in tesla (T); field lines run from north to south outside a magnet.
- Force on a current: F = BIL sinθ, where θ is the angle between the current and the field. Force is maximum when they are perpendicular and zero when parallel.
- Force on a moving charge: F = qvB sinθ; it is perpendicular to both v and B, so it provides centripetal force with radius r = mv/(qB).
- Direction is found with Fleming's left-hand rule for motors and right-hand rule for induced currents.
- Solenoid field B = μ₀nI, with μ₀ = 4π × 10⁻⁷ T m A⁻¹ and n the turns per metre.
- Magnetic flux Φ = BA cosθ, measured in webers; flux linkage = NΦ.
- Faraday's law: induced EMF ε = −N dΦ/dt. Lenz's law: the induced current opposes the change producing it.
- Motional EMF for a rod moving perpendicular to B: ε = BLv.
- Ideal transformer: Vs/Vp = Ns/Np, with input power equal to output power; it requires alternating current.
Worked example
A 0.40 m rod moves at 3.0 m/s perpendicular to a field of 0.25 T. Induced EMF = BLv = 0.25 × 0.40 × 3.0 = 0.30 V. If the rod slides on rails connected by a 1.5 Ω resistor, I = 0.30 ÷ 1.5 = 0.20 A. The opposing magnetic force is BIL = 0.25 × 0.20 × 0.40 = 0.020 N, consistent with Lenz's law.
Traps that cost marks
- Forgetting sinθ: the force is zero when the current is parallel to the field.
- Describing the induced current as opposing the flux itself rather than the change in flux.
- Using a transformer equation for direct current; transformers need changing flux.
- Confusing magnetic flux (BA) with flux density (B).
- Getting the direction wrong by mixing left-hand and right-hand rules.
- Quoting the force on a charge as along the velocity; it is perpendicular.