# Can a spherically symmetric antenna radiate?

#### Loren Booda

Seems to me I was taught in college physics that either a spherical "antenna" could not radiate or an antenna could not radiate spherically. Are either true? How about for an acoustical spherical membrane? For quadrupole mediated gravity?

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#### Hans de Vries

Gold Member
Seems to me I was taught in college physics that either a spherical "antenna" could not radiate or an antenna could not radiate spherically. Are either true? How about for an acoustical spherical membrane? For quadrupole mediated gravity?
It's the second one: "An antenna can not radiate spherically symmetrical"

The reason is ultimately the conservation of charge. If you could "switch"
a charge on and off then you would have perfectly spherical radiation.

This would however violate the conservation of charge given by $\partial_\mu J^\mu=0$,
where J is the 4-vector current. The radiation would be longitudinally
polarized, with E in the direction of the motion and without a B component.

The fact that we always can describe radiation by orthogonal E and B
fields transversal to the direction of the motion is ultimately also the
result of the conservation of charge: $\partial_\mu J^\mu=0$ leads to $\partial_\mu A^\mu=0$,
which is the conservation of the potential field. This restriction then leads
to a reduction in the degrees of freedom of the electric radiation field.

Regards, Hans

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