Chapter 1

Electrostatics and Magnetostatics

Coaxial cable

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.

If you have more questions, feel free to ask them on the forum.

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.

Coaxial cable

Question

Compute the magnetic field in any point of space.

Hint

Think about Ampère's circuital law. First do a study of the symmetry.

Solution

Symmetry and invariance studies give :

.

Let's apply Ampere's circuital law to a circle of radius that interlaces the wire.

Let's consider the cases :

  •  : (No current interlaced)

  • If  :

    Hence :

  • If  :

  • If  : (interlaced current globally equal to zero)

Question

Verify the interface conditions.

Hint

Solution

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 :

Previous
Uniform rotation of a cylinder evenly charged in volume
Next
Multiple choice quiz