On Sunday, July 27, 2014 at 1:10:02 PM UTC-4, Rich L. wrote:
I've been meditating on a question for a week or more and not seeing how to resolve it. It concerns conservation of momentum with electromagnetic forces.
Consider a wire carrying a current and a stationary charge a small distance from it. Let's assume the current is carried by negative charges moving is a static matrix of positive charges, as is usually the case. The stationary charge for now is
positive.
If the current is increasing with time, the magnetic vector potential at the stationary charge will likewise be increasing, and pointing in the same direction as the current (i.e. opposite to the actual electron motion). Because the vector potential
is increasing, there will be an electric field directed in the opposite direction. As a result the positive charge will accelerate in the same direction as the electrons.
The acceleration of the electrons will induce a "radiation resistance", which will appear as a force on the accelerating electrons that will resist the acceleration. In other words, the force required to accelerate the electrons will be slightly
greater than that required to accelerate their mass. This force is a rate of change of momentum. This extra momentum has to go somewhere, but it isn't going into the electrons.
Conservation of momentum requires that this extra momentum be accounted for. The obvious answer is that the extra momentum is transferred to the stationary charge (and other charges much further away). This works, because the stationary charge will
be accelerated in the same direction as the electrons are being accelerated, provided the stationary charge is positive.
But what about if the stationary charge is negative? In that case the charge will accelerate in the opposite direction, and its momentum will be in the opposite direction. The electrons in the wire will feel the same radiation resistance, however, so
how is momentum conserved?
Hi Rich
You had me going there for a while. I fire a cannon ball from a ship. The cannon ball leaves at 1000 MPH and the ship recoils at 1 MPH . Considering the differences in mass momentum as been conserved. Let us consider the ship to be the electrons in your
wire and the cannon ball to be the a electron or a positron sitting at a distance. The ship moves north meaning electrons are moving north causing an attractive force in an electron at right angles to this movement . The electron moves towards the moving
ship. If it were a positron it would move away from the moving ship. In both cases momentum has been conserved as the ship was also effected and changed direction. In the ships case it was much less as it has a greater mass.
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