Electromagnetic induction

This is the umbrella name for the whole effect. Faraday's law is the size of the induced emf and Lenz's law is its direction; induction is the phenomenon both of them describe.

Everything follows from what the flux is made of. AP Physics 2 gives it at 12.4.A.2 as $\Phi_B = BA\cos\theta$, and the relevant equation printed under 12.4.A.4 writes the law with that expansion left in place, $\mathcal{E} = -\Delta \Phi_B / \Delta t = -\Delta(BA\cos\theta)/\Delta t$. Three symbols sit inside the bracket, so three things can change:

• the field strength $B$, as when a magnet is pushed toward a coil;
• the area $A$ enclosed by the circuit, which is what a conducting rod sliding on rails does (12.4.A.5, with its derived $\mathcal{E} = B\ell v$);
• the orientation $\theta$ between the field and the area vector, which is a generator.

AP Physics C: Electricity and Magnetism spells out the first two as separate statements, 13.2.A.1.i and 13.2.A.1.ii, and gives induction a whole unit rather than a topic. Nothing in either course adds a fourth lever, because the flux has no fourth variable.

Nothing here needs a magnet to move. Only the flux has to change. Hold the loop still, hold the magnet still, and switch off the current that made the field, and the emf appears anyway.

Do not confuse this with [charging by induction](/glossary/charging-by-induction). That is an electrostatics procedure involving no magnetism and no rate of change. The two share a word and nothing else.

Topic 12.4 works the cases.