and

Integrating Equation (695) over a Gaussian pill-box enclosing part of the boundary surface between the two media gives

(696) |

where is the unit normal to this surface directed from medium 1 to medium 2. Integrating Equation (696) around a small loop that straddles the boundary surface yields

(697) |

assuming that there is no true current sheet flowing at the surface. In general, there is a magnetization current sheet flowing at the boundary surface whose density is given by

where is the magnetization in medium 1 at the boundary, et cetera. It is clear that the normal component of the magnetic field, and the tangential component of the magnetic intensity, are both continuous across any boundary between magnetic materials.