Chapter 3

# 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.

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