If a point charge is at rest in a frame of reference and an observer moves on an inertial frame at a velocity $\vec{v}$ with respect to the frame of reference of the point charge, according to Biot Savart's law the observer should see a magnetic field because of the moving point charge, but from the frame of reference of the charge, there is no magnetic field because the charge is at rest. How do I make sense of this contradiction. It cannot be that there is a space shared by the two frames where one sees a magnetic field and the other doesn't
Suppose we have a magnetic field directed into the computer screen. Assume that there is no gravitational field. Now suppose we have a stationary positively charged particle in the magnetic field. The magnetic force is given by $$\mathbf{F}=q\mathbf{v}\times\mathbf{B}$$  Since $\mathbf{v}=0, \mathbf{F}=0$.  Now pick a reference frame moving to the left with constant velocity. In this frame, the particle is moving to the right with constant velocity. So, the magnetic force is directed upwards.  From what I've learnt in physics, forces are independent of choice of reference frames as long as the frames are inertial. But in the 2 inertial reference frames I have chosen, I get 2 different magnetic forces. How do we reconcile this?
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