Question

A round current-carrying loop lies in the plane boundary between magnetic and vacuum. The permeability of the magnetic is equal to R. Find the magnetic induction μ at an arbitrary point on the axis of the loop if in the absence of the magnetic the magnetic induction at the same point becomes equal to B₀. Generalize the obtained result to all points of the field.

Answer 1

The medium I is vacuum and contains a circular current carrying coil with current l. The medium II is a magnetic with permeability μ. The boundary is the plane z = 0 and the coil is in the plane z = l.To find the magnetic induction, we note that the effect of the magnetic medium can be written as due to an image coil in II as far as the medium I is concerned. On the other hand, the induction in II can be written as due to the coil in I, carrying a different current. It is sufficient to consider the far away fields and ensure that the boundary conditions are satisfied there. Now for actual coil in medium l,

In the limit, when the coil is on the boundary, the magnetic field every where can be obtained by taking the current to be