# Energy flux of an EM wave

Hello,

The energy density of an electromagnetic wave is $ε_{0}E^{2}$. To calculate the energy flux, at least in the derivation's I've seen, people just multiply by the speed of the wave, i.e., c. But doesn't this assume that the energy density is constant at all points?; but E changes periodically! Why isn't it then the integral of the energy density in the corresponding volume, so it would give something close to a half of the usual answer i see!?

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Just read in here: http://hep.ph.liv.ac.uk/~hutchcroft/Phys258/CN6EMWaves.pdf [Broken] that I was right yeah. Walter Lewin's lecture was a bit missleading.

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jtbell
Mentor
One has to be very careful with terminology and keep in mind exactly which quantity is being discussed. The instantaneous power density (W/m2) passing through a surface oriented perpendicular to the wave propagation direction is indeed ε0cE2.

However, the magnitude of E oscillates rapidly between 0 and the amplitude Emax (often called E0). Finding the time-average over a whole number of cycles gives half of the maximum power density, so the time-averaged power density (which is what we can actually measure in practice) is (1/2)ε0cEmax2 which is often written as (1/2)ε0cE02.

I haven't watched Levin's lecture so I don't know which terminology he's using.