Forces like the gravitational and the electric force are in the direction of the force field. Why is it that the magnetic force is orthogonal to the velocity of the charge and the magnetic field? Was this derived or empirically verified? If the latter, then what experiments were performed, and how did the cross product perfectly fit the direction of the orthogonal vector?
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1$\begingroup$ The expression from which it follows was derived by Thomson (1881), with computational mistakes, and by Heaviside (1885) and Lorentz (1895) correctly. Lorentz also included the electric force contribution, see Wikipedia's history section. $\endgroup$– ConifoldMar 22, 2021 at 22:04
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$\begingroup$ Wasn't it discovered experimentally first? $\endgroup$– user14095Mar 25, 2021 at 23:47
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