Force due to a moving charge = qvB
Immagine a charge moving with some velocity on earth and I calculate the force due to its magnetic field with Earth as reference frame for me. An astronaut in space also calculates the force but space as reference frame.
For ease lets imagine that everything is happening in XY-plane then the force would be perpendicular to both of us, so our motion in XY plane would hove no effect on the force.
The force calculated by me and the astronaut would be different...right? If so, then how is this possible that the force produced is different when it should be same?