Mutual Induction

" We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough."
Niels Bohr
• 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 N2 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, M21,

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 M21 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  M21 = M12 .  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:
1. Determine B due to one circuit at the location of the other using Ampere's Law or the Biot-Savart Law.
2. Using this B calculate the magnetic flux through the 'other' circuit.
3. Then use the equation N2Φ2 = MI1 to obtain M.
You will always find that M depends only on the geometric parameters of the two circuits and the number of turns in each circuit.

This girl said she recognized me from the vegetarian club, but I'd never met herbivore.

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu