- #1
golfingboy07
- 17
- 0
Question: Show (mathematically) that a sphere charged in spherical symmetry ocillating radially will not radiate
My ideas so far:
We can use polar coordinates and choose a test point on the z axis so that the transvere components of J cancel. 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
My ideas so far:
We can use polar coordinates and choose a test point on the z axis so that the transvere components of J cancel. 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