A changing magnetic flux can produce an electric field around a closed path. Faraday's law relates the induced electromotive force to the rate of change of magnetic flux:

$$\mathcal E=-\frac{d\Phi_B}{dt}.$$

For a closed loop,

$$\oint_C\mathbf E\cdot d\boldsymbol\ell =-\frac{d}{dt}\int_S\mathbf B\cdot d\mathbf A.$$

Lenz's law

The minus sign expresses Lenz's law: the induced effect opposes the change in magnetic flux that produces it.

If magnetic flux through a conducting loop increases in one direction, the induced current produces a magnetic effect opposing that increase.

How flux can change

Induction can occur because the magnetic field changes, because the loop changes area, because it rotates, or because it moves through a nonuniform field.

The important quantity is the time variation of flux through the loop.

Induced electric fields

The electric field produced by changing magnetic flux is different from an electrostatic field. Its circulation around a closed path need not be zero, so it cannot generally be represented by a single electrostatic potential function.

Faraday's law is the physical basis of generators, transformers and inductors.