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Integrating Eq. 8) where K is some constant fixed by the charge, Q, and the permittivity, e0. Many methods of evaluating K exist, but we will use Gauss's Law. 9) Applying it here we choose as the surface, 5, a sphere of radius, R. On that sphere, the electric field, E, has been shown to be of constant amplitude (although always pointing in the R direction). 10) The displacement, D, on that sphere is (from Eq.

Reciprocity in circuits. In Fig. 2-3 two circuits are shown. The black box used in both is identical. The voltage, K0, imposed is in both cases the same, and the voltages Vl9 V2 are measured at the output of the respective circuits. e. Vx = V2. That is what we mean by reciprocity. This property carries over into electromagnetics where the interchange of source and observer will produce the same measured value. The second property of free space is homogeneity. e. the space coordinates. Many things contribute to inhomogeneities in materials, with the most important being the composition or structure of the material.

4) are in differential form. Historically, each equation first appeared in integral form since point by point measurements of the fields were beyond the first electromagnetic pioneers. The integral forms will now be presented. 29) The right-hand side simply gives the total charge in the region. The left-hand side is perfect for applying the divergence theorem described in Chapter 1. 30) In so many words, integrating the displacement vector, D, over any closed surface, 5, must result in a value equal to the total charge, Q, enclosed within that surface.

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