# 6.8 Boundary Conditions for Electromagnetics

In Chapters 4 and 5, we applied the integral form of Maxwell’s equations under static conditions to obtain boundary conditions applicable to the tangential and normal components of E, D, B, and H on interfaces between contiguous media (Section 4-8 for E and D and in Section 5-6 for B and H). In the dynamic case, Maxwell’s equations (Table 6-1) include two new terms not accounted for in electrostatics and magnetostatics, namely, ∂B/∂t in Faraday’s law and ∂D/∂t in Ampère’s law.

This is because, if we were to apply the procedures outlined in the previously referenced sections for time-varying fields, we would find that the combination of the aforementioned terms vanish as the areas of the rectangular loops in Figs. 4-20 and 5-24 are made to approach zero.

The combined set of electromagnetic boundary conditions is summarized in Table 6-2.

# Table 6-2 Boundary conditions for the electric and magnetic fields.

Table 6 2 Full Alternative Text

Concept Question 6-9: When conduction current flows through a material, a certain number of charges enter the material on one end and an equal number leave on the other end. What’s the situation like for the displacement current through a perfect dielectric?

Concept Question 6-10: Verify that the integral form of Ampère’s law given by Eq. (6.43) leads to the boundary condition that the tangential component of H is continuous across the boundary between two dielectric media.