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Mutual Inductance Between Two Coils Wound on an Iron Core

When a current passes through the coils of a loop of wire, a magnetic field is produced. If a second coil is wound to the first one, all 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 two long coils are wound on an iron core. A currentflows through the primary coil. This produces a fluxthrough the secondary coil. Because the secondary coil hasturns, the total flux threading the secondary coil is

The mutual inductance of the coils is then defined asIf we can treat each coil as a solenoid of lengththen the field through the centre of the arrangement is uniform and given by

Thenand