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Extra info for High Voltage Engineering - Theory and Practice
Solution ofelectricfieldproblemsby the finite-element method is based on the fact, known fromvariational calculus, that Laplace's equation is satisfied when the total energy functional is minimal. 35) where A represents the area scanned by the triangular elements. The potentials cf, at the different nodes are unknown variables and, for minimum energy functionals, Y 1 X Gridforthefinite-elementtechnique and a r r a n ~ e m e n tof the elements. 36) for all the potentials at the nodes (Silvester and Ferrari, 1983).
18) tan62 E=t2/&2 4 1 E2 On the other hand, in DC voltage applications, accumulation of free charges at the interface takes place because of the differing conductivities of the materials (interfacial polarization). 5. 18) points out that the electricdisplacementfluxlines penetrating from a dielectric of a high E into one of a much lower E are forced to leave the material nearly perpendicular to its surface. This means that the equipotential surfaces in the lower-permittivity dielectric are forced to be nearly parallel to the interface, and the dielectric of the much higher E behaves almost like a conductor as E "+ 00.
10) Thus, the unknown charges qj can be evaluated. The charges simulating a given electrode canbechosen as point charges, ring charges, oras finite, semi-infinite, or infinite line charges. This choiceshould suit the shape of the electrode being simulated. For Finite line charge Ring charge X X Contour points Arrangement of simulation charges and contour points: (b) sphere with cylindrical shank. spherically capped rod; (a) hemi- example, spherical electrodes can easilybe simulated by point charges.