Inside This Unit: The Full Breakdown
This unit covers magnetic forces on charges and currents, magnetic fields of currents via Ampère’s law, and electromagnetic induction through Faraday’s and Lenz’s laws.
Why it matters
Magnetism and induction carry the heaviest weight and reward the symmetry-based use of Ampère’s law and the calculus of Faraday’s law.
Key concepts
- The Lorentz force F = qv × B is perpendicular to velocity and field.
- Ampère’s law, ∮B·dl = μ₀I_enc, finds fields of symmetric currents.
- Magnetic flux Φ_B = ∮B·dA; Faraday’s law EMF = −dΦ_B/dt.
- Lenz’s law fixes the direction: induced current opposes the change in flux.
Magnetic Forces and Ampère’s Law
A magnetic field exerts F = qv × B on moving charges (circular motion when perpendicular) and F = ∫I dl × B on currents. With symmetry, Ampère’s law gives fields directly: B = μ₀I/(2πr) for a long wire and B = μ₀nI inside a solenoid.
Electromagnetic Induction
A changing magnetic flux induces an EMF by Faraday’s law, EMF = −dΦ_B/dt, and Lenz’s law sets the direction so the induced current opposes the change. Motional EMF (BLv) and inductance (EMF = −L dI/dt) are key applications.
AP exam tip
For induction, compute the flux first, then differentiate for the EMF magnitude (Faraday) and apply Lenz’s law separately for the direction.
Connections to other units
- Unit 4: Induced EMFs drive currents through circuits.
- Unit 1: Ampère’s law parallels Gauss’s law as a symmetry-based field tool.
