Skin effect in a metallic conductor plunged in a solenoid
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A cylindrical solenoid of axis and radius is constituted of whorls by meter.
It is travelled by a variable current of intensity .
We admit the own magnetic field created by the solenoid is uniform inside ( ) :
And equal to zero outside ( ).
We also admit the electric field is ortho-radial :
Determine the electric field inside the solenoid
A long and massive cylinder with the same axis as the solenoid, of conductivity , height and radius is put inside the solenoid.
Determine the density of current created by the electric field .
What is the observable effect associated to these currents ?
Ohm's local law gives :
Heating due to Joule effect : let's compute the density of power
Deduce the magnetic field created by the currents on the axis.
Give the conduction under which this “induced” field is negligible in front of the one created by the solenoid.
The magnetic field created by the currents on the axis is along .
We can use Ampère's circuital law to calculate this field.
The field outside the cylinder of radius is equal to zero.
Using the closed circuit given on the figure, we can write :
The ratio of these two magnetic fields is :
In other words, , which is the skin depth.
If this condition is not verified, indicate without any justification the repartition of currents in the cylinder.