Two large parallel conducting planes carry surface current densities i1 and i2 (in A/m) flowing in the same direction. What is the magnetic force per unit area acting on each plane?

mu0 * i1 * i2 / 4
mu0 * i1 * i2 / 2
mu0 * i1 * i2
mu0 * i1 * i2 / (2*pi)

Correct answer: mu0 * i1 * i2 / 2

Solution

Plane 1 produces a magnetic field of magnitude B1 = mu0*i1/2 in the region between the planes (and outside). The force per unit area on plane 2 due to this field is F/A = i2 * B1 = mu0*i1*i2/2. By Newton's third law, plane 1 experiences an equal and opposite force.

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