Method of Analysis - wykład

Method of Analysis Because of the discontinuities in the material 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 line
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 Figure 6.1.
In the case of the surface integrals, the chosen surface is the pill box surface. In the
pill box, the large flat surfaces are of dimensions L × L and lie parallel to and on each
side of the boundary. The box has thickness t. In Figure 6.1 the large L × L surfaces are
viewed from an edge, and appear as a line.
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