The Equation of an Electromagnetic Field in a Moving Magnetically Anisotropic Conducting Medium

Abstract: In most problems concerning calculation of an electromagnetic field, it is reasonable to use vector magnetic potential (Formula presented.), which is an auxiliary function that meets the condition (Formula presented.). In vector algebra, div rot (Formula presented.) therefore, in the calculation of a field, one of the main conditions, div (Formula presented.) = 0, is always met. Since the rotor of the gradient of any scalar quantity is zero, the gradient of an arbitrary scalar is introduced into the left-hand part of the second Maxwell equation. The time derivative of this scalar is not a factor that can change magnetic and electric fields. Thus, using the basic equations of an electromagnetic field, its potentials can be determined with an accuracy equivalent to the scalar gradient. Such invariance is called the “gauge” or “gradient” invariance. To eliminate this uncertainty when finding the field potentials, they are subjected to an additional condition set by a special gauge. For an electromagnetic field propagating in vacuum, the Lorentz gauge is known; for a conducting medium, this gauge loses its meaning. When choosing a gauge for conducting media, the condition div (Formula presented.) should be met; therefore, it is reasonable to use it as a gauge one. It is shown that, in solving a one-dimensional problem, div (Formula presented.) can be taken to be zero, while a special gauge of the potential field is required in solving two- or three-dimensional problems. It is proposed to use the condition div (Formula presented.) as a gauge, since it is satisfied in all conducting media. © 2021, Allerton Press, Inc.