Lorentz
To simplify let the magnetic field point in the z-direction and vary with location x and let the conductor translate in the positive x-direction with velocity vConsequently in the magnet frame where the conductor is moving the Lorentz force points in the negative y-direction. The Lorentz force has the same form in both frames though the fields differ namely.
Lorentz Velocity Transformation
The LorentzLorenz equation is similar to the ClausiusMossotti relation except that it relates the refractive index rather than the dielectric constant of a substance to its polarizability.

. The LorentzLorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz who published it in 1869 and the Dutch physicist Hendrik Lorentz who discovered it independently.
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