Why does a uniformly charged sphere that oscillates not radiate power?

[yxgao]

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

Thanks

 

[Tide]

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

 

[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.

 

[dextercioby]

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.

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 want to know about the radiation (spectrum,power radiated,angular distribution,...).

Daniel.

 

[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!

 

[dextercioby]

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!

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!

 

[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.

 

[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?

 

[Andrew Mason]

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

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

 

[Loren Booda]

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

 

[Tide]

What if the sphere was moving at a speed v?

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