The hall voltage is created by a current in a magnetic field. Similarly, a non current carrying conductor in an electric and magnetic field will appear to have a voltage in a different reverence frame. This follows from there being non zero B in the rest frame inside the conductor, which transforms into an electric field in S´. Is this the same effect?
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In both cases - Hall voltage due to current flowing in magnetic field, and voltage due to conductor moving in magnetic field - are due to separated charges, a polarized free charge distribution on surface of the conductor.
In case of the Hall voltage, free charge concentrates on boundary of the conductor due to Lorentz magnetic forces acting on the current-forming charges, until electrostatic field of this charge inside the conductor gets strong enough to counteract those magnetic forces, and stops further concentration of surface charge.
In case of conductor moving in magnetic field it is the same principle, only magnetic forces act on all free charges inside the moving conductor, and the electric field of the surface charge moves with the conductor, so in the lab frame it is not correct to call it electrostatic.
answered Nov 26, 2023 at 16:53