A change in the magnetic field induces an electromotive force (EMF) in a coil, as described by Faraday’s Law of Electromagnetic Induction.

When the strength or direction of a magnetic field varies, it generates a changing magnetic flux through a coil of wire. This alteration in flux induces an EMF in the coil in accordance with Faraday’s Law. The induced EMF is directly proportional to the rate of change of the magnetic flux, with the constant of proportionality referred to as the mutual inductance between the coil and the magnetic field.

The induced EMF can be calculated using the formula:

where $N$ represents the number of turns in the coil, and $\frac{d\Phi}{dt}$ denotes the rate of change of magnetic flux. The negative sign in the equation signifies that the induced EMF opposes the change in magnetic flux that generates it, a concept encapsulated in Lenz’s Law.

This phenomenon underpins numerous practical applications, including generators, transformers, and electric motors. For instance, in a generator, a coil of wire is rotated within a magnetic field, leading to a change in flux that induces an EMF in the coil. In a transformer, two coils are positioned in close proximity, and a varying current in one coil produces a changing flux in the other coil, which consequently induces an EMF. In electric motors, a varying current in a coil generates a changing magnetic field that interacts with a fixed magnetic field, resulting in a torque that rotates the motor.