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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)A∴ε=∫Pdt=∫(ϵcE²)A⋅dtP =SA=(EH)A=(E(ϵcE))A=(ϵcE²)A \\ ∴ε = ∫Pdt = ∫(ϵcE²)A·dt
∵These are constants
∴ε=∫(ϵcE²)A⋅dt=(ϵE²)∫A⋅c⋅dt∴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∴ε = ϵE²·V