If tow coils are close together a changing current and magnetic field in one can induce a changing magnetic field and current in the other.
We can define the mutual inductance M by the equations,
Where
are the EMF's induced in coils 1 and 2 by the changing currents (
and
) in coils 2 and 1 respectively. Notice mutual inductance is symmetric. Similarly we can define the self inductance L of a coil:
Uses
Inductors may be used security doors and metal detectors. A coil has an alternating current passing though it. If a piece of easily magnetized metal such as iron or any material containing iron is brought into close proximity with the second coil, the induced EMF 
changes, which can be used to set off an alarm.