Why does the magnitude of magnetic force which one moving charge exerts on another charge appears inconsistent in different frames of reference?
I have a fundamental misunderstanding about the definition of magnetic force as arises from Lorenz force: . According to a basic fact of electromagnetism, electric currents are the source of magnetic fields, and a single moving charge can be viewed as a current. Therefore, in a situation of one moving charge and another stationary charge, the moving charge creates a magnetic field, but by the Lorenz definition of magnetic force, the force experienced by the stationary charge iz zero (since it's velocity is zero). But if we shift to a frame of reference moving at half the speed () of the first charge and in the same direction, we get one charge moving in a speed and a second charge moving at . In this scenario, the magnetic force experienced by the same charge is not zero.
So what exactly am i missing? i view it as a serious bug in my fundamental understanding of electromagnetism, and i will be extremely thankful if someone will complete for me the picture of charge-charge electromagnetic interaction.