#electric current density

[peeterjoot]

Maxwell equation boundary conditions in media

Maxwell equation boundary conditions in media

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Following [1], Maxwell’s equations in media, including both electric and magnetic sources and currents are

\begin{equation}\label{eqn:boundaryConditionsInMedia:40} \spacegrad \cross \BE = -\BM – \partial_t \BB \end{equation} \begin{equation}\label{eqn:boundaryConditionsInMedia:60} \spacegrad \cross \BH = \BJ + \partial_t \BD \end{equation}

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[peeterjoot]

Duality transformation

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In a discussion of Dirac’s monopoles, [1] introduces a duality transformation, forming electric and magnetic fields by forming a rotation that combines a different pair of electric and magnetic fields. In SI units that transformation becomes

\begin{equation}\label{eqn:dualityTransformation:40} \begin{bmatrix} \boldsymbol{\mathcal{E}} \\ \e…

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[peeterjoot]

Reciprocity theorem: background

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The class slides presented a derivation of the reciprocity theorem, a theorem that contained the integral of

\begin{equation}\label{eqn:reciprocityTheorem:360} \int \lr{ \BE^{(a)} \cross \BH^{(b)} – \BE^{(b)} \cross \BH^{(a)} } \cdot d\BS = \cdots \end{equation}

over a surface, where the RHS was a volume integral involving the fields and…

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