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.
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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
.
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.
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 :
