EASA / CAR Part-66 · Module 3 · 3.11 Inductance & Inductors · Cat B1/B2
Objective: show that a changing magnetic flux linking a coil induces an EMF, e = −N dΦ/dt, and that the induced current always opposes the change that produced it, which is Lenz's law.
Flux through the coil is increasing, so the induced current flows in the direction that creates a magnetic field opposing the approach.
An EMF is induced in a coil only while the magnetic flux linking it is changing. A stationary magnet, however strong, induces nothing: hold the magnet still and the EMF falls to zero even though the flux itself is large. That is the single most common misunderstanding in this topic, and it follows directly from the derivative in e = −N dΦ/dt.
The magnitude of the induced EMF depends on three things: the number of turns N, because each turn links the flux and the EMFs add in series; the strength of the field, which sets how much flux there is to change; and the rate of change, which is why moving the magnet faster produces a larger EMF even though the peak flux is unchanged.
The minus sign is Lenz's law. As the magnet approaches, the induced current circulates so that the coil presents a like pole to the magnet and repels it. As the magnet withdraws, the current reverses so the coil attracts it, trying to hold the flux constant. Either way the induced effect opposes the change, which is a statement of conservation of energy: the work done pushing the magnet against that opposition is what becomes electrical energy. This is exactly how a generator produces power, and why generators become harder to turn as electrical load increases.