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I am thinking about the problem, "Why does a group of charges with spherical symmetry, where each oscillates radially while retaining spherical symmetry, not radiate?" I figured out that with a spherically symmetric charge distribution, there only exists a monopole scalar potential which is time-independent. However, I do not have any clue about what spherical symmetry implies for the magnetic vector potential. Can anyone give me some ideas about this?

Qmechanic
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Kim Jinwoo
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1 Answers1

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Radiation would have to be spherically symmetric. Both the E and B vectors would have to be radial. Suppose either had a tangential component at some point. If you rotate the system around the axis through that point and the center, everything should look the same. You should also see a component in the rotated direction. You can't have two non-zero tangential vectors at the same point. The tangential component has to be zero.

But that means E and B are parallel. That isn't possible for radiation.

mmesser314
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