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.
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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 :
Compute the electromotive force induced by the current .
There are two magnetic fields, hence two fluxes to compute.
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 :
Compute the ratio :
can be neglected before .
Use complex notation.
The electric equation of the circuit is :
Which is, in complex notation :
can be neglected before :
With a magnitude for of , intensities can be measured with ammeters of small caliber.