By Dragan Poljak
This article combines the basics of electromagnetics with numerical modeling to take on a large diversity of present electromagnetic compatibility (EMC) difficulties, together with issues of lightning, transmission traces, and grounding structures. It units forth a fantastic origin within the fundamentals earlier than advancing to really good issues, and permits readers to advance their very own EMC computational versions for purposes in either study and undefined.
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The surfaces ÁS of the volume are assumed to be arbitrarily small so that the normal ﬂux density Bn does not vary across the surface. Also, the thickness of the disk is vanishingly small so that there is negligible ﬂux through the side wall. Starting from the fourth Maxwell equation in the integral form, I ~ Bd~ S¼0 ð2:109Þ S stating that magnetic ﬂux is always zero for closed surfaces it follows: I ~ Bd~ S ¼ B1n ÁS À B2n ÁS ð2:110Þ S Now, if the disk surfaces approach one another, keeping the interface between them, the net outward ﬂux from the disk is B1n ÁS À B2n ÁS ¼ 0 ð2:111Þ B1n ¼ B2n ð2:112Þ or TEAM LinG 31 BOUNDARY RELATIONSHIPS FOR DISCONTINUITIES IN MATERIAL PROPERTIES In other words, the normal component of magnetic ﬂux density is continuous across an interface.
5 Region 1 Electric ﬂux density at the boundary between two different media. where, Z Q¼ rs dS ð2:99Þ S The side integral approaches zero if the disk thickness goes to zero. 100) one obtains D1n ÁS À D2n ÁS ¼ rs ÁS ð2:101Þ D1n À D2n ¼ rs ð2:102Þ or With the direction information included, where n is the unit vector normal to the surface, ~1 À D ~2 Þ ¼ rs ~ nð D ð2:103Þ The boundary conditions at an interface between two regions with different permeabilities can be found in the same way as was done for the case of different permittivities.
12 FUNDAMENTALS OF ELECTROMAGNETIC THEORY RETARDED POTENTIALS The potential wave equations can be solved completely in a relatively small number of special cases. 161) are given in the form of so-called retarded potentials. Assuming that the solution of the potential wave equation r2 j À ms qj q2 j rðtÞ À me 2 ¼ À qt qt e ð2:166Þ is desired in the unbounded space, the charge density rðtÞ differs from zero only in an inﬁnitesimal space dV surrounding the origin. Namely, the right-hand side represents a time-varying point charge.