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### Magnetic Dipole and its Radiation Field

Consider radiation emitted from two magnetic dipoles. Have them be two circular loop antennas each of area of aligned parallel to the -plane with center on the -axis. Fix their location in Rindler sectors and by having them located at and so that they are accelerated into opposite directions. Suppose each antenna has proper current

Then its magnetic moment is

its charge-flux four-vector obtained from Eq.(29) is
 (59)

and the corresponding scalar source function for Eq.(27) is
 (60)

Here is the Heaviside unit step function. The proper magnetic dipole is the proper volume integral of this source,

Being symmetric around its axis, such a source produces only radiation which is independent of the polar angle . Consequently, all partial derivatives w.r.t. vanish, and the full scalar field, Eq.(54), in becomes with the help of Eq.(47)
 (61)

where

This is the T.E. scalar field due to a localized pair of axially symmetric loop antennas, each one with its own time dependent current. By setting one of them to zero one obtains the radiation field due to the other.

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Ulrich Gerlach 2001-10-09