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Magnetic field due to current element

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Question

A system consists of two parallel planes carrying currents producing a uniform magnetic field of induction B between the planes. Outside this space there is no magnetic field. The magnetic force acting per unit area of each plane is found to be B2Nμ0. Find N.

Moderate
Solution

Let J be the current per unit length. 

B=2μ0J2=μ0J

Magnetic field due to one plane - B/2

 Force on other plane F=B2Jl1l2 This force is on the shaded part.  Force per unit area: Fl1l2=B2J=B2Bμ0=B22μ0 Hence N = 2

 


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