# Homework Help: Why does a uniformly charged sphere that oscillates not radiate power?

1. Dec 16, 2004

### yxgao

Why does a uniformly charged sphere that oscillates between two radii at a certain frequency not radiate power?

Thanks

2. Dec 16, 2004

### Tide

The simple answer is that outside the sphere (distances greater than the larger radius) the electric field is constant.

3. Dec 16, 2004

### yxgao

Does the radiation only depend on the electric field outside of the sphere? Where can I find the expression of the power radiated?

Why does it not depend on other variables, such as the frequency of oscillation, or the radius?

Thanks for any replies.

4. Dec 16, 2004

### dextercioby

Applying Gauss's law,u find that,in the exterior of the sphere,the (electric) field is constant,BUT ONLY IN THE WHEN CASE THE (CHARGED) SPHERE STANDS STILL.If it moves,then it should be treated like any other moving charge and it will definitely radiate electromagnetic energy.You'll have to supply the frequency of the oscillations of the sphere and u can use classical theory of radiation (v.J.D.Jackson/L.D.Landau,E.Lifschitz) to estimate everything u wanna know about the radiation (spectrum,power radiated,angular distribution,...).

Daniel.

5. Dec 16, 2004

### yxgao

So it does not matter that the sphere is constantly changing frequency? I haven't studied this topic in detail before. Is there an online reference that gives an introduction and relevant equations?

Thanks!

6. Dec 16, 2004

### dextercioby

The fact that the frequency is not constant,but varying in time complicates the problem even more.
I don't know an good reference online for the theory of radiation,and especilally this kind of problem,except some CED courses as a whole.Which comprise a chapter of the theory of radiation as they should.

This is the famous free online course:
http://www.plasma.uu.se/CED

It's pretty good.Not comparable to J.D.Jackson's,but i think it should provide you with an idea about em radiation.

Daniel.

PS.Calcuations are not that easy.Beware!!

Last edited by a moderator: Apr 21, 2017
7. Dec 17, 2004

### Tide

Dexter,

I don't think the sphere will radiate. You are thinking of the Larmor formula for radiation by an accelerated charge but there is no component to the radiation field in the direction of the acceleration. Because the charge distribution is spherically symmetric there is no dipole component to the fields. There may be higher order components to the field (quadrupole, etc.) but there is no dipole field.

8. Dec 18, 2004

### yxgao

Is this correct: The sphere does not radiate because it is at rest and the charge is constant. Outside of the sphere, the electric field is constant. Radiation only depends on the rate of change of electric field. Therefore, the sphere does not radiate.

What if the sphere was moving at a speed v?

9. Dec 18, 2004

### Andrew Mason

If the charge redistributes itself constantly as the radius changes so that $\sigma$ is uniform over the sphere at all times at all radii, there is no time dependent electric field. The only way the charge could redistribute itself that quickly is if the sphere was made of metal.

How do you get a metal sphere to oscillate its radius (and, therefore, surface area) and still keep the metal sphere intact? So I think this question deals with a theoretical situation, and is not a phenomenon that anyone has observed.

AM

10. Dec 18, 2004

### Loren Booda

Does there exist a configuration of oscillating charges that radiates isotropically? How about a configuration of oscillating masses?

11. Dec 18, 2004

### Tide

If it were moving at a constant velocity then, no, it will not radiate. It will radiate only if it undergoes acceleration.