Calculating Magnetic Energy Between Plates

[Roger Dalton]

Homework Statement

Hello everyone!

Please, could anybody help me solving this exercise? I have some doubts about if my approach is correct:

Two infinite and parallel thin sheets carry equal surface current densities (1 A / m2), uniform and constant. The space between the sheets is occupied by a material of relative magnetic permeability 3. Calculate the pressure exerted on this material if A) The currents circulate in the same direction, B) if they circulate in n opposite directions.

Thanks in advance!

Relevant Equations

F = -grad(U_m)

The current density between the plates is J = 1 A/m2. So, I have to calculate first the magnetic energy in the whole space. Out of the sheets, there is no current, so the magnetic energy would be 0 in that places. Hence,

U = J(1/2) \int_{inside the plates}A(r)dr, where A(r) is the vector potential inside the plates.

Then, I would apply F = -grad(U), and as the pressure is F/S, I'll get the answer. Would it be correct? However, I don't know how to do that with matter between them.

 

[kuruman]

The first approach I would try is not through the vector potential. I would use Ampere's law to find the magnetic intensity $H$ inside the material, use it to find the energy density $u$, use it to find the energy inside a box of area $A$ and height equal to the plate separation. I think you know how to proceed from here.

Note: This is another old unanswered thread to be removed from the "unanswered" list.