Question: Show (mathematically) that a sphere charged in spherical symmetry ocillating radially will not radiate(adsbygoogle = window.adsbygoogle || []).push({});

My ideas so far:

We can use polar coordinates and choose a test point on the z axis so that the transvere components ofJcancel. For radiation to occur (using the coulomb gauge) there must be a transverse component of the current density vector to drive it. Since this is not the case the sphere charged in spherical symmetry will not radiate. How do I go about proving this mathematically? Is my physical statement even correct?

Thanks

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# Radiation theory

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