What is the correct frame of reference for determining the magnetic force on a charge?
If two charges are both stationary in a given inertial frame, F1, then neither charge should experience a magnetic force due to the presence of the other charge (qv = 0). If we accelerate one charge, but not the other, then again, neither charge should experience a magnetic force, since only one charge has a non-zero velocity as measured in that inertial frame, meaning the other, stationary charge will experience no force in the magnetic field of the moving charge.
Now imagine that we are riding along as part of another inertial frame, F2, and that the first inertial frame discussed above that contains the two electrons F1, is traveling at a relative velocity of v from our perspective (i.e., it’s moving faster than us). Now imagine that we fire two electrons from our inertial frame F2, towards F1, one that travels at a velocity of v from our perspective, thereby traveling at the same velocity as the electron that appeared stationary in F1, and another that travels at the same velocity as the second, "faster" electron.
From our perspective in F2, both electrons have a non-zero velocity: the “slow one” traveling at a velocity of v, and the “fast one” traveling a bit faster than that. From our perspective, in F2, both electrons should experience a magnetic force of attraction due to their non-zero velocities in non-zero magnetic fields, which would change the path of those electrons from the perspective of both inertial frames.
However, from the perspective of F1, the “slow” electron is stationary, and should not experience any magnetic force in any magnetic field.
This seems to not make sense - what would happen as an experimental matter?