- As we have seen, Faraday's Law of Induction tells us that a changing magnetic flux through a circuit will induce an emf and therefore an "induced current". Consider the situation of two nearby circuits (below) where the flux through circuit 2 changes due to the changing current in circuit 1.

- With N
_{2}turns in circuit 2 the emf is given by

but the total flux through circuit 2 is proportional to the current in circuit 1, where the proportionality constant is called the mutual inductance of the coils, M_{21},

Combining these two equations gives

In other words the emf in circuit 2 is proportional to the rate of change of current in circuit 1. As we will see shortly, the mutual inductance M_{21}depends only on the geometric configuration of the two circuits.

- If the roles of the two circuits are reversed - that is a changing current in circuit 2 induces a current in circuit 1 - then

- It is "easy" to show that M
_{21}= M_{12}. In other words given two circuits in a particular configuration it doesn't matter in which circuit the current is induced the mutual inductance is the same.

**UNITS:**Inductance is measured in Henrys

The concept of inductance is related to the magnetic field in a similar way that capacitance is related to the electric field.

- In order to calculate mutual inductance you will typically follow the steps below:

You will always find that

- Determine
Bdue to one circuit at the location of the other using Ampere's Law or the Biot-Savart Law.- Using this
Bcalculate the magnetic flux through the 'other' circuit.- Then use the equation N
_{2}Φ_{2}= MI_{1}to obtain M.M depends only on the geometric parameters of the two circuits and the number of turns in each circuit.

*Dr. C. L. Davis*

*Physics Department*

*University of Louisville*

*email*: c.l.davis@louisville.edu