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  • How is the shape of a nominally spherical extended charge modified by a

    From john mcandrew@21:1/5 to All on Fri Mar 13 17:36:01 2020
    The Coulomb field of a charge is modified by a gravitational field:

    https://en.wikipedia.org/wiki/Paradox_of_radiation_of_charged_particles_in_a_gravitational_field#Resolution_by_Rohrlich

    So I'd expect it to be similarly modified by a Rindler space, together with a corresponding change in the shape of the extended charge: is there a name for this shape, if it's spherical when not accelerated?

    I think this example shows how rigidness needs to be carefully handled in classical electrodynamics. It also means that the idea of a constant rest mass for an accelerated extended charge, compared to at constant velocity, has to be carefully modelled
    through internal forces maintaining the correct proper frame shape, and not to make hasty assumptions about it.

    John McAndrew

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  • From john mcandrew@21:1/5 to john mcandrew on Tue Mar 17 17:07:12 2020
    On Saturday, March 14, 2020 at 12:36:02 AM UTC, john mcandrew wrote:
    The Coulomb field of a charge is modified by a gravitational field:

    https://en.wikipedia.org/wiki/Paradox_of_radiation_of_charged_particles_in_a_gravitational_field#Resolution_by_Rohrlich

    So I'd expect it to be similarly modified by a Rindler space, together with a corresponding change in the shape of the extended charge: is there a name for this shape, if it's spherical when not accelerated?

    I think this example shows how rigidness needs to be carefully handled in classical electrodynamics. It also means that the idea of a constant rest mass for an accelerated extended charge, compared to at constant velocity, has to be carefully modelled
    through internal forces maintaining the correct proper frame shape, and not to make hasty assumptions about it.

    John McAndrew

    A clue comes from looking at the fields for a hyperbolic accelerated charge, figure 3 here: https://www.reed.edu/physics/faculty/griffiths/Hyperbolic.pdf

    If the charge is "rigid", then the surface should be equipotential, normal to the field lines. Here, one half looks like a compressed ellipse, the other expanded by the same factor; but this is just a guess.

    John McAndrew

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  • From john mcandrew@21:1/5 to john mcandrew on Tue Mar 17 17:19:46 2020
    On Saturday, March 14, 2020 at 12:36:02 AM UTC, john mcandrew wrote:
    The Coulomb field of a charge is modified by a gravitational field:

    https://en.wikipedia.org/wiki/Paradox_of_radiation_of_charged_particles_in_a_gravitational_field#Resolution_by_Rohrlich

    So I'd expect it to be similarly modified by a Rindler space, together with a corresponding change in the shape of the extended charge: is there a name for this shape, if it's spherical when not accelerated?

    I think this example shows how rigidness needs to be carefully handled in classical electrodynamics. It also means that the idea of a constant rest mass for an accelerated extended charge, compared to at constant velocity, has to be carefully modelled
    through internal forces maintaining the correct proper frame shape, and not to make hasty assumptions about it.

    John McAndrew

    A clue comes from looking at the fields for a hyperbolic accelerated charge, figure 3 here: https://www.reed.edu/physics/faculty/griffiths/Hyperbolic.pdf

    If the charge is "rigid", then the surface should be equipotential, normal to the field lines. I had assumed that one half would be a compressed ellipse, the other expanded by the same factor; but the figure shows that the equipotential surface is in
    fact a circle!

    Hence there is a rearrangement of the surface charge density along the surface of the sphere, becoming concentrated at the leading edge compared to the trailing edge.

    John McAndrew

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