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=Pdtε = ∫Pdt

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

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

∵These are constants

ε=(ϵcE²)Adt=(ϵE²)Acdt∴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=ϵE²V∴ε = ϵE²·V