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The 'impedance of free space is written like this, too, as the absolute value of the $E$-field over the absolute value of the $H$-field.

What does the ratio of the strengths of the two fields of an electromagnetic wave have to do with the impeding of their propagation through space?

Also, the impedance of a wave through a dielectric is sometimes written as the square root of the permeability constant (mu) over the permittivity constant (epsilon)... Why? Why is the number related to the magnetic field now on top, and the electric number on bottom?

Qmechanic
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Kurt Hikes
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1 Answers1

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Well... from a purely dimensional analysis perspective the electric field $\vec E$ is measured in $V/m$ (Volts per meter) and the magnetic field $\vec H$ in $A/m$ (Ampères per meter). Thus the ratio is $V/I$, which like the resistance $R$ in $V=RI$ is just an impedance.

As to the second part of your question, the ratio of amplitudes of $\vec E$ to $\vec H$ follows from Maxwell's equation. The specific form of the ratio (in terms of $\epsilon$ and $\mu$) actually depends on the choice of units so there's no obvious way of justifying $\sqrt{\mu_0/\epsilon_0}$ other than solving M's equations or observing that this ratio has the dimensions of $V/A$ so that \begin{align} \frac{E}{H}=\sqrt{\mu_0/\epsilon_0} \end{align} in vacuum.

ZeroTheHero
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