Question about energy density in On the Electrodynamics of Moving Bodies

[e2m2a]

In section 8 of Einstein's On the Electrodynamics of Moving Bodies Einstein uses
the expression A(sq)/8 pi. He states this represents the energy of light per unit volume. Does anyone know how he derived this?

 

[jtbell]

It comes from classical electrodynamics, and Einstein undoubtedly viewed it as a "well known" relationship. You can find derivations in many current textbooks, where it usually looks different because we use different units nowadays for electromagnetic quantities, than Einstein did. In MKS units we usually write it as

$$\langle u \rangle = \frac{1}{2} \epsilon_0 E_0^2$$

where $E_0$ is the amplitude (maximum magnitude) of the electric field in a light wave, $\epsilon_0$ is a constant (the same one that appears in Coulomb's Law in MKS units, if you're acquainted with it), and <u> is the average energy density. (The instantaneous energy density oscillates as the wave oscillates, so we usually talk about the average value which is what we measure in practice anyway.)