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Method of Analysis

Because of the discontinuities in the materiał parameters, and the discontinuities in at least

some components of the electromagnetic field which result therefrom, Maxwell's equations

in differential form fail, in the sense that the derivatives do not exist, at the boundary.

Maxwell's equations in integral form, however, still apply, as such finite

discontinuities

are readily integrable.

Maxwell's equations in integral form involve two contour integrals and two surface integrals. The method of analysis is to apply those equations to particular integrals over

special contours or surfaces appropriately chosen in relation to the boundary. For the linę

integrals, the chosen contour is a safety pin loop of length L and thickness t of which one

long side lies on each side of the boundary. This loop is shown in Figurę 6.1.

In the case of the surface integrals, the chosen surface is the pili box surface. In the pili box, the large fiat surfaces are of dimensions L x L and lie parallel to and on each side of the boundary. The box has thickness t. In Figurę 6.1 the large L x L surfaces are viewed from an edge, and appear as a linę.