By Dragan Poljak

This article combines the basics of electromagnetics with numerical modeling to take on a wide diversity of present electromagnetic compatibility (EMC) difficulties, together with issues of lightning, transmission strains, and grounding structures. It units forth an effective beginning within the fundamentals earlier than advancing to really expert subject matters, and permits readers to enhance their very own EMC computational types for purposes in either examine and undefined.

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This equation is known as Lagrange equation of motion. Hamilton variational principle can be considered as a general law not only for particle dynamics but also for the dynamics of continuous materials. 186) is given by Zt2Z d "d dVdt ¼ 0 L ð2:190aÞ t1 V "d is so-called the Lagrange density deﬁned by where L Z L¼ "d dV L ð2:190bÞ V and has a unit of energy per volume. It is worth noting that the variational principle is an invariant scalar equation for coordinate transformations [3]. 2 Lagrangian Formulation and Hamilton Variational Principle in Electromagnetics In an electromagnetic oscillation, energy oscillates between electric and magnetic energy just as in a mechanical oscillation energy oscillates between kinetic and TEAM LinG 46 FUNDAMENTALS OF ELECTROMAGNETIC THEORY potential energy.

Namely, the right-hand side represents a time-varying point charge. 167) is that the potential still corresponds to the charge causing it, but with a time retardation which equals the time taken for light to propagate from the charge to the point of potential observation. The electrostatic potential, on the contrary may be viewed simply as the special case of very small retardation, that is, a simpliﬁcation valid at close distances. 167) can be applied to the more general case of time-varying charge distributed over some ﬁnite volume of space V by dividing the volume into small portions and treating the charge in each as a point charge at the given point.

91) are the equation of motion of electromagnetic waves in free space. The velocity of wave propagation is the velocity of light, TEAM LinG 26 FUNDAMENTALS OF ELECTROMAGNETIC THEORY 1 c ¼ pﬃﬃﬃﬃﬃ me ð2:92Þ where c ¼ 3 Â 108 m=s, approximately. 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.