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Does anybody know why an unifarmly charged sphere does not emite if its radius changed arbitrariby?

It's known that accelarated charge emits but there is no radiation in my example.

Any help here would be appreciated.

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Where did you run across this claim?

Arbitrarily changing the radius of a sphere seems unphysical.

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Also, I don't see how you could have a sphere of charge change its radius while keeping it uniformly charged. Uniformly in space while the charge density changes with time?

Any "realistic" model I can think of would produce radiation, as compressing the charge to a smaller volume would produce repulsion, and thereby, acceleration.

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38 minutes ago, joigus said:

Also, I don't see how you could have a sphere of charge change its radius while keeping it uniformly charged. Uniformly in space while the charge density changes with time?

Any "realistic" model I can think of would produce radiation, as compressing the charge to a smaller volume would produce repulsion, and thereby, acceleration.

There seems to have been some discussion of this topic on the physics stack exchange some years ago, the conundrum being that the electric field lines, beyond the boundary of the sphere, are unaffected by a purely radial change. At least, I think that's what it was all about.

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36 minutes ago, joigus said:

Also, I don't see how you could have a sphere of charge change its radius while keeping it uniformly charged.

I’m assuming this means a uniform spatial distribution, not a constant value. But a uniform distribution is what you expect if it’s a conductor.

If you simply reduced r of each charge, the energy goes up, so work must be done. You would have to do this at the limit of zero speed, otherwise the start and stop require a radial acceleration

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2 hours ago, swansont said:

Where did you run across this claim?

Arbitrarily changing the radius of a sphere seems unphysical.

I'm fairly sure I could make a balloon out of conductive rubber and put a motorised pump inside it to move air in and out of a cylinder (also within the balloon).
It's absurd, but not unphysical.

As long as it stayed spherical, I can't see what polarisation any resulting radiation would have. That's going to make it hard to emit photons.

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10 minutes ago, John Cuthber said:

I'm fairly sure I could make a balloon out of conductive rubber and put a motorised pump inside it to move air in and out of a cylinder (also within the balloon).
It's absurd, but not unphysical.

But it wouldn’t be a perfect sphere, and the asymmetry is likely the issue here.

Quote

As long as it stayed spherical, I can't see what polarisation any resulting radiation would have. That's going to make it hard to emit photons.

That’s the issue, I think. The motion is radial and so is the field, and you would need a transverse component of the field to emit radiation. Which may become possible if the spherical symmetry is broken.

(I have a vague recollection of an example in Griffiths of a problem where the energy of a system and the work required to assemble it are unequal, implying energy had to be lost from the system, i.e. from radiation. Can’t recall if it was this example, though)

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1 hour ago, swansont said:

But it wouldn’t be a perfect sphere, and the asymmetry is likely the issue here.

That’s the issue, I think. The motion is radial and so is the field, and you would need a transverse component of the field to emit radiation. Which may become possible if the spherical symmetry is broken.

(I have a vague recollection of an example in Griffiths of a problem where the energy of a system and the work required to assemble it are unequal, implying energy had to be lost from the system, i.e. from radiation. Can’t recall if it was this example, though)

In the discussion I read elsewhere, there was some talk of whether the electric field, although it does not change beyond the boundary of the sphere, might change in a way consistent with radiation in the region between its greatest and least radial extent. Though, weirdly, such radiation would not, apparently, escape. I'm not enough of a physicist to know if this makes any sense.

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Posted (edited)
6 hours ago, BratK said:

Does anybody know why an unifarmly charged sphere does not emite if its radius changed arbitrariby?

It's known that accelarated charge emits but there is no radiation in my example.

My intuitive answer is that your example is about shell theorem. If I remember correctly: Assume a sphere S with charge Q on the surface. Then the electric field outside the sphere of charge is like that of a point charge; the field outside the sphere does not rely on the radius R of the sphere S.

Shell theorem implies that another sphere S2 with same charge Q but different radius R2 will have the same field outside as the first sphere S. I do not know if the shell theorem accounts for the dynamics if a single sphere is uniformly modified* to have a different radius but identical center. If the shell theorem holds, so that the behaviour is at all times modelled by a stationary point charge, then there should be no radiation? Did the example contain one sphere changing its radius or two different spheres with identical charge on their surfaces?

*) I do not assume that such movement is practically possible, just that the uniform charge Q stays uniform on the surface while R is changed and the whole sphere stays stationary relative the observer.

Edited by Ghideon
clarified sentence
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Posted (edited)
5 hours ago, BratK said:

Does anybody know why an unifarmly charged sphere does not emite if its radius changed arbitrariby?

It's known that accelarated charge emits but there is no radiation in my example.

Any help here would be appreciated.

No the change is not quite arbitrary.

Here is a potted history of pusating charge spheres and other non radiating distributions, originally introduced by Ehrenfest.

Note these are not pulsars  With these, the effects observed are due to rotation.

42 minutes ago, exchemist said:

In the discussion I read elsewhere, there was some talk of whether the electric field, although it does not change beyond the boundary of the sphere, might change in a way consistent with radiation in the region between its greatest and least radial extent. Though, weirdly, such radiation would not, apparently, escape. I'm not enough of a physicist to know if this makes any sense.

Yes there has been discussion on other forums in  the last couple of years.

Google has various images of the physics of the explanation, going back to 'all' will find the PhysicsForums and Stack discussions

Edited by studiot
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27 minutes ago, Ghideon said:

Shell theorem implies that another sphere S2 with same charge Q but different radius R2 will have the same field outside as the first sphere S. I do not know if the shell theorem accounts for the dynamics if a single sphere is uniformly modified* to have a different radius but identical center. If the shell theorem holds, so that the behaviour is at all times modelled by a stationary point charge, then there should be no radiation? Did the example contain one sphere changing its radius or two different spheres with identical charge on their surfaces?

If it’s a conducting sphere, the field will now exist in the region between R1 and R2. (There’s no field inside a conducting sphere) Which has to be the case, since you have to do work to compress the charge, and (some or all of) that energy gets stored in the field.

36 minutes ago, studiot said:

Google has various images of the physics of the explanation, going back to 'all' will find the PhysicsForums and Stack discussions

You’d expect dipole radiation, but dipoles don’t radiate along their axis. Symmetry suggests any tangential radiation should cancel. The presence of a radiation pattern would contradict the symmetry.

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3 hours ago, swansont said:

But it wouldn’t be a perfect sphere, and the asymmetry is likely the issue here.

We are, pretty much, discussing the spherical cow in a vacuum here.

Yes, in practice it wouldn't be perfect, but in principle, it works.

Would it "sort of radiate" because the normal BBR would be blue or red shifted, meaning that it would reflect more or less than would be "expected"?

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Posted (edited)
1 hour ago, studiot said:

No the change is not quite arbitrary.

Here is a potted history of pusating charge spheres and other non radiating distributions, originally introduced by Ehrenfest.

Note these are not pulsars  With these, the effects observed are due to rotation.

Yes there has been discussion on other forums in  the last couple of years.

Google has various images of the physics of the explanation, going back to 'all' will find the PhysicsForums and Stack discussions

Yes the "Skulls in the Stars" article seems to deal with it. Good old Ehrenfest, again!

So it's false to assume that any accelerating charge must always radiate, apparently: symmetry can trump that general rule.

Edited by exchemist
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I'm glad @John Cuthber and @swansont took this thread in the right direction after my faltering start. Very interesting link from @studiot too. I agree it's all in the symmetry. You would have to have, e.g., non-spherical fluctuations in charge, to have any radiation at all.

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