Does anyone know of a reference that finds the fields of a charged sphere moving in a constant magnetic field?already well known but I can't see it mentioned in Jackson or Griffiths as a problem.
My initial thoughts is that there will be a constant circulating current of non-uniform charge density induced in the sphere which becomes a static polarized electric field in its rest frame. It's an interesting problem so I'm pretty sure this is
On 21/02/13 12:20 AM, john mcandrew wrote:already well known but I can't see it mentioned in Jackson or Griffiths as a problem.
Does anyone know of a reference that finds the fields of a charged sphere moving in a constant magnetic field?
My initial thoughts is that there will be a constant circulating current of non-uniform charge density induced in the sphere which becomes a static polarized electric field in its rest frame. It's an interesting problem so I'm pretty sure this is
You don't say it's an accelerated sphere this time! So then I
think it essentially is in Jackson. You certainly can find the transformation of the B-field to the sphere's rest frame there
(where indeed a electric component will be present which will
create a static polarization of the sphere).
But also, it should be clear from Jackson how you then can
transform back the polarized sphere to the frame in which the
sphere is moving (and there you'll still have nothing more than
a static polarization and no circulating current, if the sphere
is not superconducting at least..)
The case may not be explicitly mentioned but all you need for
it is there. (Now if you could make it a uniformly accelerated
sphere it might be more interesting.. in that case I'd also
expect a combination of circulating current and increasing
static polarization.)
On Sunday, February 14, 2021 at 8:26:37 PM UTC, Jos Bergervoet wrote:already well known but I can't see it mentioned in Jackson or Griffiths as a problem.
On 21/02/13 12:20 AM, john mcandrew wrote:
Does anyone know of a reference that finds the fields of a charged sphere moving in a constant magnetic field?
My initial thoughts is that there will be a constant circulating current of non-uniform charge density induced in the sphere which becomes a static polarized electric field in its rest frame. It's an interesting problem so I'm pretty sure this is
Hence there's three magnetic fields: the external B, B_v from the sphere moving at velocity v, and B_p from the polarized surface rotating around the center of the sphere.You don't say it's an accelerated sphere this time! So then I
think it essentially is in Jackson. You certainly can find the
transformation of the B-field to the sphere's rest frame there
(where indeed a electric component will be present which will
create a static polarization of the sphere).
But also, it should be clear from Jackson how you then can
transform back the polarized sphere to the frame in which the
sphere is moving (and there you'll still have nothing more than
a static polarization and no circulating current, if the sphere
is not superconducting at least..)
The case may not be explicitly mentioned but all you need for
it is there. (Now if you could make it a uniformly accelerated
sphere it might be more interesting.. in that case I'd also
expect a combination of circulating current and increasing
static polarization.)
I had in mind the charged sphere moving freely in the magnetic field B with initial velocity v so that it moves in a circle (spiral taking into account the radiation), accelerated by the net Lorentz force qvxB and slowly losing velocity from radiation.
Another question: what happens as we reduce the bare mass of the sphere so it becomes entirely electromagnetic?a constant electric field E. But as a guess: the circulating polarized current I_p is gradually reduced to zero, giving a uniform, static surface charge distribution.
The effect of the retarded self EM field on the rotating polarized surface charge now has to take into account the retarded magnetic field B_r, which makes things more complicated than the previous case we discussed for the charged sphere accelerated by
JMcA
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