11.4.1 Interface Conditions for the Electric Field
To derive the interface conditions, we assume two different materials with properties as shown in Figure 11.2a.We assume
a surface charge density ρs at the interface between the two different materials and apply Eq. (11.28). Because Eq. (11.28) is
a closed contour integral, we choose a closed contour that includes the interface alone, with two sides parallel to the interface
and two sides perpendicular to the interface. The integration is in the direction shown. The closed contour is formed by the
segments ab, bc, cd, and da: