Place two coils near one another. A current in one coil generates a magnetic field that passes through the second coil. Changing the current in the first coil changes the magnetic flux through the second, inducing an emf in the second coil. This is known as mutual inductance, inducing an emf in one coil by changing current somewhere else. The induced emf can be written:

e

=

– N

DFB Dt

=

– M21

DI Dt

The constant M₂₁ is the mutual inductance, which depends on various factors, including the area and number of turns in coil 2, the distance between the coils, their relative orientation, the number of turns / unit length in the first coil, and whether the coils have ferromagentic cores. In other words, M₂₁ is rather complicated, in general. One situation where it's actually easy to calculate is when the two coils are wrapped around the same ferromagnetic core, so all the flux generated by the first coil passes through the second.

One practical use is in a transformer, a device that converts AC electricity from one voltage to another. Another use is as an ammeter. Usually ammeters are placed in series in a circuit, but some AC ammeters are simply loops placed around wires. An emf proportional to the current will be induced in the loop because of the changing magnetic field from the wire.