# Can a spherically symmetric antenna radiate?

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?

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