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In the previous section, we examined the radiation emitted by a short electric dipole of oscillating dipole moment

(1116) 
where
. We found that, in the far field, the mean
electromagnetic energy flux takes the form [see Eq. (1094)]

(1117) 
assuming that the dipole is centered on the origin of our spherical polar coordinate system.
The mean power radiated into the element of solid angle
, centered on the angular coordinates (, ),
is

(1118) 
Hence, the differential power radiated into this element of solid angle is
simply

(1119) 
This formula completely specifies the radiation pattern of an oscillating electric dipole (provided that the dipole is much shorter in length than the
wavelength of the emitted radiation). Of course, the power radiated into
a given element of solid angle is independent of , otherwise energy would not be conserved. Finally, the total radiated power is the integral of
over all solid angles.
Next: Thompson scattering
Up: Electromagnetic radiation
Previous: The Hertzian dipole
Richard Fitzpatrick
20060202