22.9 Electromagnetic Waves (continued)

EM Wave Energy Density u

The energy density u_el, the energy per volume, stored in a sinusoidally varying electric field E is

u_el= (electric energy)/volume = (1/2) e_o E²

The energy density u_mag, the energy per volume, stored in a sinusoidally varying magnetic field B is

u_magg = (magnetic energy)/volume = [1/(2 µ_o)] B²

Therefore, the total energy density u of the electromagnetic wave is the sum of these,

u = (1/2) e_o E² + [1/(2 µ_o)] B²

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 E²

or

u = (1/µ_o ) B²

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 intensity of 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 E²

or

S = (c/µ_o) B²

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(c) Doug Davis, 2002; all rights reserved