# Stationary charge in varying magnetic field

Usually this issue is examined in loops, coil etc with currents. I am referring to a realistic situation that can be easily tested in places like LHC.

Suppose there is a charge moving at near (.999999991) c approaching and overtaking a stationary charge A (minimum distance = 1 cm): the magnitude of the electric/magnetic field will increase until A is overtaken, an then it rapidly decreases.

Do you know if A will oscillate or move at all because of the magnetic force? If it does, by what law and formula , and, in what direction?

Edit:

I am asking about the effects of a varying magnetic field, if the example above can cause misunderstandings, please substitute the approaching charge with a magnet.

## 2 Answers

Classically a sitting charge q should feel the Lorentz force of the fields of the approaching Q

One would have to model the approaching and distancing E and B but I would just expect a scattering, no oscillations.

• Since A has v=0, Lorenz force is zero. But when the charge is approacing its magnetic field increases, so another law should be at play (Faraday/Lenz?) (besides the ordinary electrostatic attraction/repulsion). When the charge overtakes A and passes on, the magnetic field decreases and the effect (if any) would be rereversed, so, all in all, A should just bob, oscillate once, like a cork on water when a wave is passing. – user137879 Mar 14 '17 at 8:15
• That "$\times$" cross product symbol can be easily confused for $x$ – Apoorv Potnis Mar 14 '17 at 8:16
• @lambertwhite Its velocity is zero before the Q is close,at the approach the electric field of the Q will induce an attractive or repulsive motion to q by its electric field, which will give a v to q which will then interact with the B of the moving Q. Lorenz force is enough, but complicated . – anna v Mar 14 '17 at 9:27
• @ApoorvPotnis the image is copied from the hyperphysics link. A physicist should not be confused, between two vectors there is either a dot or a cross procuct. – anna v Mar 14 '17 at 9:29
• Why are you excluding an effect of B on A when v=0? why does an increasing Bfield have an effect on the charges in a piece of metal? it is not due to Lorenz, is it? Electric force will make A move away from/toward Q in a parallel direction so Lorenz force will be zero – user137879 Mar 14 '17 at 11:11

Elastic scattering between free charges due to electromagnetism was first performed by Rutherford.

In order to preserve total momentum, any momentum change $\Delta \vec p_c$ in the moving particle must be balanced by a change $\Delta \vec p_A = -\Delta \vec p_c$ in the momentum of the (initially) stationary particle. However if the incident and target masses are dissimilar, the momenta may match without very much change in the velocity of the less-massive particle.

• Are you hinting that there is a collision? – user137879 Mar 14 '17 at 5:51
• One usually discusses the "impact parameter"; the link is a good starting point. – rob Mar 14 '17 at 5:53