where B ¼ μH was used to obtain the second relation from the first.
The interface conditions for the magnetic field may be summarized as follows:
(1) The tangential component of the magnetic field intensity is discontinuous in the presence of surface current densities.
The discontinuity is equal to the surface current density. In the absence of surface current densities, the tangential
component of the magnetic field intensity is continuous across the interface.
(2) The tangential component of the magnetic flux density is discontinuous.
The interface condition in Eq. (11.56) assumes the magnetic field intensity only has one tangential component or that
each tangential component is treated separately. We have faced the same issue in Section 9.3.1. To establish a more general
relation, we note from Figure 11.2 that the tangential components of the magnetic field intensity may be written as H1t
¼ n^ H1 ½A=m and H2t ¼ n^ H2 ½A=m where n^ points into material (1) [see Eq. (9.42)]. With these observations,
Eq. (11.56) is written as [see Eq. (9.42)]: