Maxwell’s Equations

Abstract

AbstractTime-varying currents and charges are known to produce time-varying electromagnetic fields. Time-varying electromagnetic fields are governed by Faraday’s law and Ampère’s law, which are two fundamental equations in electrodynamics. Two additional Gauss’s laws can be derived from Faraday’s law and Ampère’s law. A set of Faraday’s law, Ampère’s law, and two Gauss’s laws is referred to as Maxwell’s equations. In this chapter, we will discuss time-varying electromagnetic fields using Maxwell’s equations. Script letters (\(\overline{\mathcal{E}}\), \(\overline{\mathcal{H}}\), \(\overline{\mathcal{D}}\), \(\overline{\mathcal{B}}\), \(\cdots \)) will be used for time-varying quantities.KeywordsContinuity equationAmpère’s lawMaxwell’s equationsBoundary conditionsPoynting’s theoremVector potentialHelmholtz’s equation