# Electromagnetic induction

# Clamp ammeter

Take 15 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.

The usual ammeters cannot bear high intensities (in general )

To measure higher intensities, a clamp ammeter is used.

The principle is studied here.

An infinite straight wire of axis is travelled by a current (the one we want to measure) of intensity :

The wire is surrounded by a winding made of a square-section torus of side a and medium radius .

On the torus are regularly wound a great number of whorls.

This winding is closed on an ammeter.

The circuit created has a total resistance and is travelled, by induction, by a sinusoidal current :

## Question

Compute the electromotive force induced by the current .

### Hint

There are two magnetic fields, hence two fluxes to compute.

### Solution

The magnetic field due to the infinite wire is (apply Ampere's law), at a point inside the torus :

The own magnetic field of the torus is (apply Ampere's law) :

The total magnetic field is :

The flux of this total field through the whorls of the torus is :

Hence the electromotive force can be deduced by using Faraday's law of induction :

## Question

Compute the ratio :

can be neglected before .

### Hint

Use complex notation.

### Solution

The electric equation of the circuit is :

Which is, in complex notation :

Thus :

can be neglected before :

With a magnitude for of , intensities can be measured with ammeters of small caliber.