Re: [Phys-L] Fwd: Can you please post this electrostatics question to Phys-L listserv?

[John Denker <jsd@av8n.com>]

On 2/3/19 10:47 AM, Bob Sciamanda via Phys-l wrote:
>     'Does an operating  high speed commercial ultracentrifuge produce an
> electric field between the rotor hub and the  sample holder because
> electrons are flung outward?  The centrifuge develops 100.000 g's  (quite a
> large acceleration).'
>
>     I suggested  the answer was yes in that there is a free electron gas
> within the metal and these would be influenced by centrifugal force [in the
> rotating reference frame, of course].  I'm  guessing that it's determined
> in value as being the strength of  the electric field that balances the
> outward centrifugal force.  But I can't determine how to prove this or
> calculate a result.   Also  I can't find anything on the web about this.
> Any  thoughts?"

1) The answer is yes, for all the reasons given above.

2) In particular, yes, in the rotating frame:
 -- Force from electrical field balances force from centrifugal field.
 -- You know the field at every point, so integrate to get the voltage.

 This is first cousins to the argument in high-school physics books that
 there cannot be any field inside a conductor:  Otherwise the charges
 would move, until they null out the field.  But in this case they null
 out the *overall net* force.

 This is not quite high-school physics, because it analyzes things using a
 rotating frame, which is taboo in most high-school classes.  Remember: the
 centrifugal field exists in a rotating reference frame and not otherwise.
 This technique has been around since 1687 at least.  Newton used it in the
 _Principia_ to estimate the figure of the earth, which is nonspherical due
 to rotation.

 It's a teensy bit trickier than that, because the field affects the lattice
 of ion cores also, but let's not worry about that.

3) You can google for "electron sound" in metals and/or plasmons in metals.
 The situation of interest is essentially a plasmon mode in the zero-frequency
 limit.