Magnetism and Electromagnetism
Core concepts
Magnetic fields from currents (Biot–Savart, Ampère's law), force on a moving charge (F = qv × B) and on a current-carrying wire (F = BIL sinθ), electromagnetic induction (Faraday's and Lenz's laws), self and mutual inductance, and the behaviour of magnetic materials (dia-, para-, ferro-). You should also know the Lorentz force and motion of charged particles in magnetic fields.
Traps
- Forgetting the sine of the angle between velocity and field; force is zero when they are parallel.
- Misapplying Lenz's law - the induced current opposes the change in flux, not the flux itself.
- Confusing magnetic flux (Φ = BA cosθ) with flux density (B).
- Using the right-hand rule incorrectly for electron versus positive charge.
- Assuming magnetic field lines do work on a moving charge - they do not, since force is perpendicular to velocity.
Rule of thumb
For a charge moving in a uniform magnetic field, the radius of the circular path is r = mv/(qB). The period T = 2πm/(qB) is independent of speed.
Worked example
An electron (m = 9.1×10⁻³¹ kg, q = 1.6×10⁻¹⁹ C) moves at 2×10⁶ m/s perpendicular to a 0.5 T field. r = mv/(qB) = (9.1×10⁻³¹ × 2×10⁶)/(1.6×10⁻¹⁹ × 0.5) ≈ 2.3×10⁻⁵ m, about 23 μm.