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The electric field from a ball-bearing carrying a static electric charge, is presumeably spherical. What happens to that field shape if I spin the ball? Surely at some distance,

$d > c/w $, ( where c is the speed of light and w is the angular velocity )

from the ball-bearing, the field would have to be travelling in a circle faster than the speed of light, and that's not possible! So does the field come to a stop at this distance? does it gradually 'spiral' as it approaches d or what?

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  • $\begingroup$ What do you mean surely at school me distance? Like the ball is traveling in a circle or is spinning on it's axis? Are you able to attempt the calculation on your own and show your work where you get stuck or do you not do physics on the regular? $\endgroup$
    – Triatticus
    Feb 21 at 3:47
  • $\begingroup$ Does Gauss’ Law have angular velocity in it? Are you under the impression that Gauss’ Law doesn’t apply to a spinning charge distribution? $\endgroup$
    – Ghoster
    Feb 21 at 4:23
  • $\begingroup$ @Ghoster, well then the same question but with a magnetic field, eg a bar magnet, spinnning with its north-south axis as the axis of rotation. at some distance d the magnetic field would have to be moving faster than the speed of light or the magnetic field lines would have to 'spiral' or something. I have no idea. $\endgroup$
    – pete
    Feb 21 at 5:12
  • $\begingroup$ Neither happens. $\endgroup$
    – Ghoster
    Feb 21 at 5:24
  • $\begingroup$ @Triatticus I do not do physics on the regular and remember little from the physics I used to. I'm thinking if I had a perfectly rigid stick of length r, and held it out laterally and wished to swing it round (like a skater on ice) my maximum angular velocity would be limited to below c/r, otherwise the other end f the stick would be travelling faster than the speed of light! And I'm supposing the same happens to magnetic and electroc field lines. I have never coe accross this question and have not idea what how or if the field gets 'distorted'. do you? $\endgroup$
    – pete
    Feb 21 at 5:25

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Your intuition about field lines taking time to change because information travels at the speed of light is correct for accelerating charges, not for charges moving as a constant velocity. There’s a great animation of the field of an accelerating point charge at this link.

For your example of a rotating sphere with a surface charge density, note that it will have the same electric field as a stationary charged sphere by Gauss’s law. However, the rotating surface charges constitute a current as well, and thus you would be able to calculate a magnetic field generated by the rotating sphere by treating it as a surface current density.

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