Today's post is a little plain Jane, (as far as I know), in that it's just a review of our classes' derivation of the boundary conditions for the electrical displacement field at an interface between two materials. Here's a question. Does anyone know of anything, cool or clever to take away from the following derivation? At the moment, it seems necessary, but not tantalizing. First, we'll need the Divergence Theorem, (picture 1), stating that the volume integral of the divergence of a vector field is equal to the surface integral of the same field with respect to the normal of the surface that bounds the volume. Given the above tools, and starting with a boundary between two materials, and the typical pillbox, (picture 2), where delta A is the area of the top and bottom of the box, n is the unit vector normal to the top of the pillbox and the pillbox straddles the boundary between the two materials. In the end we'll let the sides of the pill...