Question

Electrodynamics.

Consider a linear medium where $\rho$ and $\vec{J}$ are both zero in the region of interest.

$\blacklozenge$ Show that the Maxwell's equations are invariant to the transformation

where is a dimensionless constant and $\alpha$ is a constant but arbitrary angle. In other words, if $\vec{E}$ and $\vec{B}$ are solutions of Maxwell's equations, show that $\vec{E'}$ and $\vec{B'}$ too.

$\blacklozenge$ Consider the special case $\alpha =\frac{\pi}{2}$ and thus show that, in this sense, the fields $\vec{E}$ and $\vec{B}$ can be interchanged.

This property is often named the duality property of the electromagnetic field.

Step by step process with good handwriting, please. Thank you.

cos α cos α

Answer 1

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