Magnetism and electromagnetic induction
Magnetism and electromagnetic induction
This domain tests magnetic forces on moving charges and currents, the field of wires and solenoids, and induction through changing flux. Typical questions combine a right-hand rule with a calculation of motional emf, or ask for the direction of an induced current.
Core rules
- Magnetic force: F=qvB sinθ is perpendicular to both v and B; F=BIL sinθ for a current-carrying wire. The magnetic force does no work on a charged particle, so its speed stays constant.
- Field patterns: a long straight wire gives B=μ0I/(2πr); a solenoid gives B=μ0nI. Magnetic field lines are closed loops.
- Flux and Faraday's law: Φ=BA cosθ and induced emf ε=−N dΦ/dt. Change B, A or orientation to induce emf.
- Lenz's law: the induced current opposes the change in flux, not necessarily the motion itself.
- Motional emf: a rod of length L moving at speed v perpendicular to B gives ε=BLv. The induced current then experiences a force BIL that opposes the motion.
- Transformers: V_s/V_p=N_s/N_p for an ideal transformer; power is conserved.
Worked example
A 0.50 m rod moves at 4.0 m/s perpendicular to a 0.20 T field on rails connected by a 0.10 Ω resistor. The emf is ε=BLv=0.20×0.50×4.0=0.40 V. The current is I=0.40/0.10=4.0 A. The magnetic force on the rod is F=BIL=0.20×4.0×0.50=0.40 N, opposite the motion. Mechanical power needed is Fv=0.40×4.0=1.6 W, equal to electrical power I²R=16×0.10=1.6 W.
Traps
Using the left hand for a negative charge or forgetting to reverse the force direction; treating the magnetic force as capable of changing speed; using the total field instead of its perpendicular component in Φ=BA cosθ; saying Lenz's law opposes motion rather than flux change; expecting induction when flux is constant.