homework and exercises - A charged sphere with pulsing radius

Radius increases and decreases periodically (as a pulse).And so does the charges on the surface of sphere.

I can't get what is gonna happen.the EM waves are produced perpendicularly to motion of the charges,but here where is the perpendicular ? Will the EM waves get produced into the space of sphere?

Also, can two EM waves intersect each other or not? [as Electric fields lines can't intersect.]

Answer

The electric field due a uniformly charged sphere with its radius increasing at a constant rate at any point outside the sphere is the same as if the radius were not changing at all. In this scenario, you can still invoke the radial symmetry argument and use the Gauss's law along with invariance of electric charge to obtain the electric field which turns out to be the same as that of a point charge at the centre of the sphere.

Any change in the rate of increase of radius of the sphere does not lead to a change in the electric field at any point farther from the sphere than the maximum radius the sphere can attain while it is pulsating. So the electric field at all points whose distance from the centre of the sphere is larger that the maximum radius that can be attained by the pulsating sphere is constant over time. So beyond the maximum attainable radius there is no electromagnetic radiation.

However, I think there will be some electromagnetic radiation in the region between the minimum attainable radius and the maximum attainable radius. This could be in the form of standing waves confined to that region.

At any point whose distance from the centre of the sphere is less than the minimum attainable radius, I think you can again apply the above mentioned logic and conclude that there is to electromagnetic radiation in that region.

So, to conclude, I feel there should be no net electromagnetic radiation emanating from the sphere.

P.S. I have not done a detailed study of electromagnetic radiation. So, I'm not sure if the above analysis is correct. I'd be glad if somebody were to post the correct analysis of the scenario in question.