Note that in Eq. (11.29), the integration for current is a surface integration because, in general, J is a current distributed
over a volume. However, here, the current is distributed over a surface; therefore, the integration is on the line ab. The closed
contour integral of Hdl always equals the current enclosed by the contour. Note also that the contribution to the line
integral due to displacement current densities is zero. This can be best understood from the fact that as we approach the
interface, the area enclosed by the contour abcda tends to zero, and, therefore, the surface integral over the volume current
density ∂D/∂t tends to zero. Choosing ab ¼ cd, we get