# How to derive the energy of a electromagnetic plane wave

Saturday, March 10, 2018 at 04:51

Energy of a E-M plane wave on a detector:

$ε = ∫Pdt$

∵For a plane wave, S is constant over the area, so:

$P =SA=(EH)A=(E(ϵcE))A=(ϵcE²)A \\ ∴ε = ∫Pdt = ∫(ϵcE²)A·dt$

∵These are constants

$∴ε = ∫(ϵcE²)A·dt = (ϵE²) ∫A·c·dt$

∵·c·dt is the length and A is the area

∫A·c·dt gives a volume

$∴ε = ϵE²·V$