Theoretical problem (no calculations) with electric field from moving charge

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SUMMARY

The discussion centers on the electric field generated by a moving point charge, specifically a charge q moving at relativistic speed v along the x-axis. The key contention is whether the electric field at a distant point Pa, after the charge has decelerated to rest, reflects the charge's last known position or its new stationary position at the origin. The professor asserts that the field at Pa behaves as if the charge continued moving until the information of its stop propagates, while the student argues that Pa should perceive the field of a moving charge that decelerates and stops at the origin, albeit with a time delay. The phenomenon of aberration is also mentioned, indicating that the electric field at a distant observer points to where the charge will be if it continues moving.

PREREQUISITES
  • Understanding of electric fields generated by point charges
  • Familiarity with relativistic effects in physics
  • Knowledge of electromagnetic wave propagation
  • Basic concepts of magnetism and its relation to electric fields
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  • Study the implications of relativistic speeds on electric fields
  • Research the concept of aberration in electromagnetic theory
  • Explore the mathematical formulation of electric fields from moving charges
  • Learn about the propagation of changes in electric fields and their effects on distant observers
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Students in physics courses, particularly those studying electricity and magnetism, as well as educators and professionals seeking to deepen their understanding of electric fields from moving charges and relativistic effects.

solarboy
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Homework Statement



I'm in a physics 2 (electricity and magnetism) course, and I'm having trouble with something the professor discussed in class. I tried approaching him about it afterwards, but it still didn't make sense to me. I really think he made a mistake here, and I'd like input.
we're discussing magnetism, and as a precursor to that we're discussing electric fields generated by moving charges. so we have a point charge q moving at a relativistic speed v to the right on the x-axis. ( Relativistic effects make the electric field more powerful in directions perpendicular to the x-axis than parallel to the x-axis, but otherwise I don't think the prof mentioned anything that depended on the speed being relativistic- I think I qould have the same problem for non-relativistic speeds.) Fine.
At t=t0, the charge is at some negative point on the x-axis p0 (all space and time coordinates are in a stationary reference frame). at t=t1, the charge is at the origin. at that point, the charge decelerates over the extremely brief period dt to v=0.
we began discussing what happens as the effects of the stop propagate (at the speed of light, of course), and this is where I got lost. we're looking at the field at time t2 at a point Pa which is farther away than c(t2-t1) such that the effect has not has time to reach Pa yet.
My professor's version: at t2, the field within distance c(t2-t1)is that of a stationary point charge at the origin. outside, the information that the charge has stopped moving has not reached Pa yet. therefore, the field at Pa is as though the charge had continued moving, so at t2, the field at Pa is that of a moving point charge at v(t2-t1) on the x-axis. when the information that the charge stopped gets to Pa, it will suddenly shift, in Pa's perspective, from being at a positive point on the x-axis to being at the origin. (he did not discuss any relativistic effects, like changing time or location coordinates, other than the boosted field in the y direction.)
My version: at t2, the field within distance c(t2-t1)is that of a stationary point charge at the origin. outside, the information that the charge has stopped has not reached Pa, but neither has the information that the charge is at the origin reached Pa. therefore, Pa will feel the field of a moving charge somewhere left of the origin and will observe it move, decelerate, and stop at the origin in the same way as it actaully did, just with a time delay.
so should I apply for his job?
 
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His job is secure for the moment.

There is an effect called aberration for such a moving charge that makes it so the electric field at a distant observer points ahead to where the charge will be if it keeps moving. Weird but true. This is why the professor says the apparent position of the charge snaps back.
 

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