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?
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.