Fig 5.4

Equation 5.27 (a) says that tangential component of electric field is continuous across the interface while from 5.27 (c) we note that tangential component of the magnetic field is discontinuous by an amount equal to the surface current density. Similarly 5.27 (b) states that normal component of electric flux density vector is discontinuous across the interface by an amount equal to the surface current density while normal component of the magnetic flux density is continuous.
If one side of the interface, as shown in fig 5.4, is a perfect electric conductor, say region 2, a surface current can exist even though is zero as.