Electrostatics and Magnetostatics
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A detailed solution is then proposed to you.
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Let's consider an infinite cylindrical coaxial cable of radii .
The total intensity goes in one way through the interior conductor and comes back in the other way through the exterior conductor.
Let us suppose the current is evenly distributed in the volume of the interior conductor, and distributed on the surface of the exterior conductor.
Compute the magnetic field in any point of space.
Verify the interface conditions.
We notice that the field is continuous in and in (property of a volume distribution of currents).
In : the magnetic field is discontinuous, and :
The surface density on the cylinder of radius is expressed by :
The interface conditions are verified during the crossing of a surface travelled by a surface current :