# Mutual Inductance

If, on the other hand, the current in the inner solenoid is varied, the field due to it which is non-zero only within the inner solenoid. The flux enclosed by the outer solenoid is, therefore,

If is varied, the emf in the outer solenoid is giving

One can see that .

This equality can be proved quite generally from Biot-Savart's law. Consider two circuits shown in the figure.

The field at , due to current in the loop (called the *primary *) is

where . We have seen that can be expressed in terms of a vector potential , where

, by Biot-Savart's law

The flux enclosed by the second loop, (called the *secondary *) is

Clearly,

It can be seen that the expression is symmetric between two loops. Hence we would get an identical expression for . This expression is, however, of no significant use in obtaining the mutual inductance because of rather difficult double integral.

Thus a knowledge of mutual inductance enables us to determine, how large should be the change in the current (or voltage) in a primary circuit to obtain a desired value of current (or voltage) in the secondary circuit. Since , we represent mutual inductance by the symbol . The emf in the secondary circuit is given by , where is the variable current in the primary circuit.

Units of is that of Volt-sec/Ampere which is known as Henry (h)