Magnetism and electromagnetism
The magnetism block covers magnetic forces on charges and currents, fields produced by simple current distributions, Ampère's law, and electromagnetic induction. The exam usually expects correct directions as well as magnitudes, so right-hand rules and Lenz's law are examined as often as formulas.
Core rules
- Lorentz force: F = q(E + v×B). The magnetic part is perpendicular to v and B and does no work; it changes direction, not speed. A straight wire in a field experiences F = BIL sinθ.
- Long straight wire: B = μ₀I/(2πr), with circular field lines given by the right-hand grip rule. A solenoid has B ≈ μ₀nI inside.
- Ampère: ∮B·dl = μ₀I_enclosed. Use it only with sufficient symmetry.
- Magnetic flux: Φ = B·A = BA cosθ. Faraday's law: emf = -dΦ/dt. Lenz's law says the induced current opposes the change in flux.
- Motional emf for a rod of length L moving at speed v perpendicular to B: emf = BLv.
Worked example
A long straight wire carries I = 5.0 A. At r = 0.10 m, B = (4π×10⁻⁷)(5.0)/(2π×0.10) = 1.0×10⁻⁵ T. A proton moving at 2.0×10⁵ m/s parallel to the wire feels no magnetic force because v is parallel to B. If it moves perpendicular to the field, F = qvB = (1.6×10⁻¹⁹)(2.0×10⁵)(1.0×10⁻⁵) = 3.2×10⁻¹⁹ N, directed by the right-hand rule. If the wire current is switched off in 0.050 s, a nearby loop would experience an induced emf proportional to the rate of change of flux, with the current direction opposing the decrease.
Traps
Use the correct right-hand rule: thumb along current, fingers curl with B. For a negative charge, reverse the force direction. Do not say magnetic force does work or changes kinetic energy. In induction, the induced current opposes the change in flux, not necessarily the original field. Flux depends on angle: cosθ = 1 when B is perpendicular to the loop area. Keep area in m² and time in seconds. A changing current in one coil induces emf in another only while the flux is changing.