How does a change in magnetic field induce an EMF in a coil?

A change in magnetic field induces an EMF in a coil through Faraday's Law of Electromagnetic Induction.

When a magnetic field changes in strength or direction, it creates a changing magnetic flux through a coil of wire. This changing flux induces an electromotive force (EMF) in the coil, according to Faraday's Law. The EMF is proportional to the rate of change of the magnetic flux, and the constant of proportionality is known as the mutual inductance of the coil and the magnetic field.

The induced EMF can be calculated using the equation EMF = -N(dΦ/dt), where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux. The negative sign indicates that the induced EMF opposes the change in magnetic flux that produced it, according to Lenz's Law.

This phenomenon is the basis for many practical applications, such as generators, transformers, and electric motors. In a generator, a coil of wire is rotated in a magnetic field, causing a changing flux and inducing an EMF in the coil. In a transformer, two coils are placed in close proximity, and a changing current in one coil induces a changing flux in the other coil, which in turn induces an EMF. In an electric motor, a changing current in a coil produces a changing magnetic field, which interacts with a fixed magnetic field to produce a torque that rotates the motor.