How Is Energy Flux Calculated in an Electromagnetic Wave?

[guillefix]

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!?

Thanks in advance

 

[guillefix]

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

 

[jtbell]

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 E_max (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)ε₀cE_max² 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.