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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)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
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