By Urban Cegrell
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Additional info for Capacities in Complex Anaylsis (Aspects of Mathematics)
It is conventional to select one equipotential body as a reference and designate its voltage as zero. The potentials of the other bodies are then specified with respect to the reference. As a simple example of finding the terminal relations for an electric field system, consider the two equipotential bodies in Fig. 6. We assume that the voltage v is impressed between the two equipotential bodies and wish to find the current i. We choose a surface S (see Fig. 26). The only current density on the surface S occurs where the wire cuts through it.
5) are fH. 22) E'" dl = - d B - n da. 23) The contours C, surfaces S, and unit normal vectors n are defined in the conventional manner, as shown in Fig. 1. The surfaces of integration S Fig. 1 (a) Surface S enclosed by the contour C, showing the right-handed relationship between the normal vector n and the line element dl; (b) surface S enclosing a volume V. The normal vector n is directed outward, as shown. 23) are enclosed by a contour C. 23 are valid even when the contours and surfaces are deforming, as demonstrated in Appendix B.
12) dt Fig. 12 Geometry for analyzing the translation of a rigid body.
Capacities in Complex Anaylsis (Aspects of Mathematics) by Urban Cegrell