# How to derive the energy of a electromagnetic plane wave

Saturday, March 10, 2018 at 04:51

$ε = ∫Pdt$

∵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 $∴ε = ϵE²·V$