This paper reviews the electromagnetic gauges and discusses the new continuity gauge in detail. It is shown that by introducing a complex Laplace's equation instead of a real Poisson's equation, the new gauge circumvents the difficulty of dealing with an unknown charge density as in the case of the Coulomb gauge. Justification is given for employing a differential rather than an integral equation formulation when working with the new gauge. Two problem scenarios are described in the formalism of the continuity gauge to explain how the new gauge can be used to solve low and high frequency electromagnetic field problems.
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