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Theoretical problem (no calculations) with electric field from moving charge 
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#1
Apr1011, 08:08 AM

P: 4

1. The problem statement, all variables and given/known data
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 xaxis. ( Relativistic effects make the electric field more powerful in directions perpendicular to the xaxis than parallel to the xaxis, 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 nonrelativistic speeds.) Fine. At t=t0, the charge is at some negative point on the xaxis 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(t2t1) such that the effect has not has time to reach Pa yet. My professor's version: at t2, the field within distance c(t2t1)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(t2t1) on the xaxis. 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 xaxis 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(t2t1)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? 


#2
Apr1011, 02:12 PM

P: 1,781

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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