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What are the boundary conditions for and at
the interface between two magnetic media? The governing equations for a steadystate situation are

(870) 
and

(871) 
Integrating Eq. (870) over a Gaussian pillbox enclosing part of the
interface between the two media gives

(872) 
where denotes the component of perpendicular to
the interface.
Integrating Eq. (871) around a small loop which
straddles the interface yields

(873) 
assuming that there is no true current sheet flowing in the interface.
Here, denotes the component of parallel to the
interface.
In general, there is a magnetization current sheet flowing
at the interface whose density is of amplitude

(874) 
In conclusion, the normal component of the magnetic field
and the tangential component of the magnetic intensity are both
continuous across any interface between magnetic media.
Next: Boundary value problems with
Up: Dielectric and magnetic media
Previous: Ferromagnetism
Richard Fitzpatrick
20060202