# [Physics] Origin of the Lorentz force from the point view of relativity

coulombs-lawelectromagnetismspecial-relativity

I'm a physicist, when I'm working on the quantum spin hall effect, I recollected the high-school knowledge on Lorentz force and try to explain the origin of it, but didn't get it in the first glance. Can anyone explain how the magnetic field interact with the moving charge more fundamentally, or, let's say, derive the equation: $\mathbf F=q\mathbf v\times \mathbf B$ in a more fundamental way?

This electric field would exert a radial force on a test charge originally at rest with respect to the wire in the stationary frame. But given that there is no radial force in the stationary frame, there cannot be a net radial force on the charge when it is in the moving frame either. The force that counteracts the radial electric field in the moving frame is the Lorentz force. Its direction is perpendicular to the velocity and the magnetic field and it's strength must be equal to $qvB$, where $B$ is the magnitude of the magnetic field in the frame moving with velocity $v$ parallel to the wire.