By Dragan Poljak

This article combines the basics of electromagnetics with numerical modeling to take on a extensive variety of present electromagnetic compatibility (EMC) difficulties, together with issues of lightning, transmission traces, and grounding platforms. It units forth a pretty good origin within the fundamentals prior to advancing to really expert themes, and permits readers to enhance their very own EMC computational types for purposes in either study and undefined.

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**Sample text**

8 BOUNDARY RELATIONSHIPS FOR DISCONTINUITIES IN MATERIAL PROPERTIES An electromagnetic ﬁeld may occur in a material medium usually characterized by its constitutive parameters conductivity s, permeability m, and permittivity e. The material is linear if s, m, and e are independent of E and H, and nonlinear if otherwise. Similarly, the medium is homogeneous if s, m, and e are not space dependent and inhomogeneous otherwise. Finally, the medium is isotropic if s, m, and e are independent of direction or anisotropic otherwise.

5 OHM’S LAW The conservation of charge in a continuous medium is expressed by the equation of continuity qr ¼0 r~ Jþ qt ð2:54Þ The current density ~ J is considered to be stationary if there is no accumulation of charge density at any point. 55) represents the ﬁeld equivalent of Kirchhoff’s current law stating that the net current leaving a junction of several conductors is zero. TEAM LinG 20 FUNDAMENTALS OF ELECTROMAGNETIC THEORY The expression which relates the current density and electric ﬁeld at any point within the conducting material is ~ J ¼ s~ E ð2:56Þ where s is the electrical conductivity of the particular material.

The minimum condition is then given by a functional F expressed [3] by the integral Zt2 Lðq; q_ ; tÞdt ¼ min F¼ ð2:181Þ t1 In classical mechanics function L is expressed as L ¼ Wkin À Wpot ð2:182Þ where Wkin and Wpot are the kinetic and potential energies, respectively. 183) respectively. Hence, it follows: Zt2 dF ¼ dLdt ð2:186Þ t1 For the simplest case given by Lðq; q_ ; tÞ, the variation of function L is given by dL ¼ qL qL dq þ dq_ qq qq_ ð2:187Þ TEAM LinG 45 THE LAGRANGIAN FORM OF ELECTROMAGNETIC FIELD LAWS Performing some further mathematical manipulation one obtains Zt2 dF ¼ t1 !