Faraday's Law

A magnet sitting still next to a coil creates a magnetic flux through that coil, but flux alone does nothing. What matters is change. Faraday's Law states that the induced emf in a coil equals the number of turns N times the rate of change of flux, emf = N delta(Phi)/delta(t). If nothing is moving and nothing is changing, delta(Phi)/delta(t) is zero, so a steady field — however strong — induces exactly nothing. This is the single most common trap in the topic: students want a big field to mean a big emf, but size of the field is irrelevant if it is not changing.

The rate matters more than the amount. A flux that changes slowly over ten seconds induces a tiny emf; the same change happening in one tenth of a second induces an emf a hundred times larger. That is why shoving a magnet into a coil quickly produces a sharp jolt of voltage, while sliding it in slowly barely registers. Double the speed of the push, and you double the rate of flux change, which doubles the emf — everything scales linearly with delta(t) in the denominator.

This sets up everything else in the unit. Lenz's Law, right after this, tells you the direction of that induced emf — it always opposes the change that caused it. Once you can find both the size from Faraday's Law and the direction from Lenz's Law, you can handle rotating coils, sliding rods on rails, and eventually the energy exchange between inductors and capacitors later in the unit.