Move a magnet near a coil and a voltage appears from nowhere. The size of that voltage is set by how fast the flux linkage changes, and its direction always fights the change.
The magnetic flux through a coil is Φ = BA, and for N turns the flux linkage is NΦ. Faraday's law: the induced e.m.f. equals the rate of change of flux linkage. Lenz's law: the induced current flows so as to oppose the change producing it, which is energy conservation in action.
As the magnet moves through the coil the flux linkage rises and falls, and the e.m.f. follows its rate of change, reversing as the magnet leaves instead of enters. Increase the speed, the turns or the magnet strength and watch the trace grow.
Instead of a magnet moving in a straight line, spin a coil of N turns in the field. The flux linkage NΦ = NBA cosθ rises and falls smoothly, and the induced e.m.f. peaks a quarter turn out of step, exactly when the coil's plane lies along the field. This is how an a.c. generator works.
Build the definitions up to Faraday and Lenz.
The e.m.f. depends on the rate of change of flux linkage, not on the flux itself: a strong magnet held still inside a coil induces no e.m.f. Always include the number of turns N (use flux linkage NΦ). Lenz's law fixes the direction, and follows from conservation of energy. For an area not perpendicular to the field, use the perpendicular component (Φ = BA cosθ).
Four quick checks on flux, flux linkage and the laws of induction. Each correct answer earns XP and lights this skill on your star map.
The magnetic flux through a flat coil of area A in a field of flux density B perpendicular to it is:
Faraday's law states that the magnitude of the induced e.m.f. is proportional to the rate of change of:
Lenz's law, that the induced current opposes the change producing it, is a direct consequence of the conservation of:
A bar magnet is held stationary inside a coil. The e.m.f. induced in the coil is:
In calculations, read the graph axes carefully: the induced e.m.f. is the gradient of a flux-linkage against time graph, so a steeper line means a larger e.m.f. Quote the e.m.f. as N ΔΦ/Δt and remember to multiply by the number of turns.
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