Consider two material systems as shown in the figure The rel

Consider two material systems as shown in the figure. The relation between the flux B and the magnetic field H and the magnetization vector M is also shown. Considering that the tangential component of the magnetic field and the normal component of the flux are continuous at the interface derive the boundary condition for the magnetic potential at the interface.

Solution

Our first boundary condition states that the tangential component of the magnetic field is continuous across a boundary. In other words:

H₁(r)=H₂(r)

The tangential component of the magnetic field on one side of the material boundary is equal to the tangential component on the other side ! We can likewise consider the magnetic flux densities on the material interface in terms of their normal and tangential components:

The second magnetic boundary condition states that the normal vector component of the magnetic flux density is continuous across the material boundary. In other words:

B₁(r)=B₂(r)

B₁(r)/u₁=B₂(r)/u₂