# Electromagnetic induction

# Mutual Inductance

Take 10 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

If you have more questions, feel free to ask them on the forum.

On a torus generated by the rotation of a circle of radius are regularly wound whorls travelled by a current .

On this winding is formed a coil made of whorls of radius .

## Question

Compute the coefficient of the mutual inductance of the two windings and .

### Hint

How is defined?

Which field is easier to compute ?

See the lesson about self inductance, mutual inductance where the magnetic field of the torus is calculated.

### Solution

The flux of the magnetic field created by the torus on the coil is :

Where is the current circulating through the torus.

Ampere's circuital law enables the determination of the field created by the torus inside. It is equal to zero outside.

To simplifiy the computation, the torus is supposed to be thin so that the magnetic field is uniform ( ).

The flux through the coil becomes :

Hence :