## EM Wave Energy Density u

The energy density u

_{el}, the energy per volume, stored in a sinusoidally varying electric fieldEisu _{el}= (electric energy)/volume = (1/2) e_{o}E^{2}The energy density u

_{mag}, the energy per volume, stored in a sinusoidally varying magnetic fieldBisu _{mag}g = (magnetic energy)/volume = [1/(2 µ_{o})] B^{2}Therefore, the total energy density u of the electromagnetic wave is the sum of these,

u = (1/2) e _{o}E^{2}+ [1/(2 µ_{o})] B^{2}For an EM wave traveling through free space, the energy stored in the electric field is equal to the energy stored in the magnetic field; that is

u _{el}= u_{mag}

And we can then write the total energy density in an EM wave as

u = e _{o}E^{2}or

u = (1/µ _{o }) B^{2}where E and B are rms values.

## EM Wave Intensity S

In addition to the energy density u, the energy per volume, of the wave, it is also useful to know about the

intensityof the wave, the power per unit area.The intensity S is given by

S = cu or, using Equations 22.25 and 22.26, the intensity can be written as

S = c e _{o}E^{2}or

S = (c/µ _{o}) B^{2}(c) Doug Davis, 2002; all rights reserved

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