By Dragan Poljak

This article combines the basics of electromagnetics with numerical modeling to take on a large variety of present electromagnetic compatibility (EMC) difficulties, together with issues of lightning, transmission strains, and grounding platforms. It units forth an excellent beginning within the fundamentals sooner than advancing to really expert themes, and permits readers to increase their very own EMC computational versions for purposes in either learn and undefined.

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**Example text**

The surface integral is taken over any surface S bounded by the loop c. 5), one obtains Z rx~ Ed~ S¼ I ~ Ed~ s ð2:6Þ c S where the line integral is taken around the loop and the integral form of the ﬁrst Maxwell equation is given by e¼À qf qt where e is an electromotive force (EMF): I Ed~ s e¼ ~ ð2:7Þ ð2:8Þ c which is effectively a voltage around the closed path and f is the magnetic ﬂux deﬁned as Z Bd~ S ð2:9Þ f¼ ~ S The voltage induced by a varying ﬂux has a polarity such that the induced current in a closed path gives rise to a secondary magnetic ﬂux which opposes the change in time-varying source magnetic ﬂux.

Therefore, the ﬁnal integral form of the conservation law in the electromagnetic ﬁeld is then given by q qt Z V 1 ~ ~ ~ ~ ðE Á D þ H Á BÞdV ¼ À 2 Z ~ E Á~ J dVþ V I ~ Þ Á d~ ð~ E xH S ð2:70Þ S In other words, the rate of increase of electromagnetic energy in the domain equals the rate of ﬂow of energy in through the domain surface less the Joule heat production in the domain. 70) is the Poyinting theorem valid for general media since there are no specializations made with respect to the medium.

Assuming the existence of net surface charge density rs on the boundary, the total ﬂux out of the disk has to equal rs . 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.