Mutual Inductance Between Two Coils

When a current passes through the coils of a loop of wire, a magnetic field is produced. If a second coil is near to the first one, some of the field lines produced by the first coil will thread through the second one. If the current through the first coil changes, so will the magnetic field. The magnetic field through the second coil will also change and an EMF will be induced in the second coil. This phenomenon is called mutual inductance – an EMF is induced in one coil because of a changing current in another. In the arrangement above a current flows through coil 1. This produces a flux (meaning the flux through coil 2 produced by the current in coil 1) through coil 2 . Because coil 2 has turns, the total flux threading coil 2 is The mutual inductance of the coils is then defined as Assuming the magnetic field produced by the current in coil 1 is uniform we may write The current at the centre of a circular loop of radius and turns carrying a current is hence then  