Relativistically, the electric field of a moving charge is not purely radially directed, but is instead concentrated perpendicular to the line of motion. So, a current loop consisting of electrons as charge carriers should generate a "charge separation" effect, where the negative electric field is concentrated perpendicular to the loop, and is not perfectly cancelled by the stationary positive ions in the (electrically neutral) conductor. Conversely, in the plane of the loop, the positive electric field should dominate. This "charge separation" effect is separate from the magnetic field produced by the current loop, as it should have the effect of accelerating stationary charges in the surrounding space, which are unaffected by a magnetic field, because their velocity is zero. I have never heard of such an effect, which should be small but measurable, hence I am asking the question.
1 Answer
So what happens is that the number of field lines emanating from a charge does not change if the charge accelerates, but the field lines concentrate to some direction.
So in the case of an infinitely long wire the number of field lines emanating from the wire does not change if the electrons in the wire accelerate.
Oh yes, the question was about a current loop. We know that in the case of a loop with infinite radius it looks like a infinitely long wire for any test charge at finite distance from the wire.
Hmm ... let us make the wire infinitely thin. And test with a test charge everywhere very close to the wire that the field has not changed, when electrons have been accelerated. (For the point-like test charge it looks like there is a infinitely long wire, right?)
So now we have shown that there is no change of the field anywhere, unless for some odd reason the field lines that are unchanged near the wire, bend so that they are changed further away.
