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?

 

[Hans de Vries]

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

 

[sir-pinski]

The statement that a spherically symmetric antenna cannot radiate is not entirely accurate. While it is true that a perfectly spherical antenna cannot radiate due to symmetry, there are ways to break this symmetry and allow for radiation. For example, an antenna with a dipole or monopole element placed off-center on a spherical surface can radiate in a non-spherical pattern.

In the case of an acoustical spherical membrane, it is possible for it to radiate sound waves in a spherical pattern. This is because the membrane is not perfectly spherical and has a non-symmetric mode of vibration.

For quadrupole mediated gravity, the concept of radiation may not apply in the same way as it does for electromagnetic radiation. However, there are theories that suggest gravitational waves can be emitted from a spherically symmetric object, such as a rotating black hole. So in this case, it is possible for a spherically symmetric object to radiate in a sense.

Overall, while a perfectly spherical antenna may not be able to radiate, there are ways to break this symmetry and allow for radiation. And in other fields such as acoustics and gravity, the concept of radiation may have different implications and behaviors.