I am studying for my quals and came across an old question that reads like the following:

There are two regions in space separated by an infinite conducting plane. Region 1 has a magnetic dipole of moment $\vec{\mu}$ located a distance $d$ from the plane. What is the magnetic field $\vec{B}$ everywhere in region 1?

I know that for a perfect conductor (superconductor), the normal component of $\vec{B}$ is zero–although I don't exactly know why–but I don't know if that is the case when the problem involves a "conductor" (not explicitly a perfect conductor).

TL;DR: Can anybody give me some insight about the magnetic boundary conditions of a stationary magnetic field in the presence of a conductor?



I believe that for an ordinary conductor, there is nothing special for a static magnetic field. But this relates only to the electrical properties of that conductor - many material have some magnetic properties as week, and those would of course modify the B field. But for the purpose of this question the B field follows the dipole field "in free space" - no modifications required.

The reason superconductors are different is that the currents initially induced by the changing B field exactly cancel the field change experienced by the conductor, and these currents don't decay. Thus the B field is "excluded" from the conductor (not just the normal component, I think - but I am willing to be wrong about that).

This is nicely described in this article about the London equations. You can convince yourself with a simple diagram that the condition "no B field inside the superconductor" is equivalent to "no normal component of B at the surface of a superconductor".


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