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Read e-book online Advanced Modeling in Computational Electromagnetic PDF

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 strains, and grounding structures. It units forth a fantastic beginning within the fundamentals prior to advancing to really expert subject matters, and permits readers to strengthen their very own EMC computational types for functions in either examine and undefined.

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Basically, this means that one should be able to set up a suitable Lagrangian function of the field variables, such that Hamilton variation principle shall result in the equations of motion of the field, that is, in Maxwell’s equations. As it is well-known, there is no general rule for the derivation of the Lagrangian function. One might be tempted to guess that it is the difference between the kinetic and potential energy of the field, but the difficulty arises as the meaning of kinetic and potentials energy in the electromagnetic field is not quite clear [3].

Basically, this means that one should be able to set up a suitable Lagrangian function of the field variables, such that Hamilton variation principle shall result in the equations of motion of the field, that is, in Maxwell’s equations. As it is well-known, there is no general rule for the derivation of the Lagrangian function. One might be tempted to guess that it is the difference between the kinetic and potential energy of the field, but the difficulty arises as the meaning of kinetic and potentials energy in the electromagnetic field is not quite clear [3].

123) can be written as the gradient of the scalar potential function j, q~ A ~ Eþ ¼ Àrj qt ð2:125Þ TEAM LinG 33 BOUNDARY RELATIONSHIPS FOR POTENTIAL FUNCTIONS or q~ A ~ E¼À À rj qt ð2:126Þ Here, A and j are usually referred as the magnetic vector potential and electric scalar potential, respectively. 126). There are also many magnetostatic problems concerned with finding magnetic fields, in which at least a part of the domain of interest is free of electric currents. For such source-free domains, the curl of the magnetic field H is equal to zero, ~¼0 rxH ð2:127Þ Since any zero-curl vector can be represented in terms of the gradient of a scalar function, the magnetic field intensity for such cases may be written as ~ ¼ Àrjm H ð2:128Þ where the minus sign is taken to provide a convenient analogy with the case of electrostatic potential.

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