In the planetary model of an atom (however invalid), the electrons rotating around the proton are discrete charges moving in a circular motion, which means that there is a finite current in a circular loop. This current leads to a magnetic field perpendicular in direction to the plane of rotation of the electron, via the Biot-Savart law. Then, is there a fundamental reason why the motion of the electrons is not modeled as a charged particle in a crossed electro-magnetic field, leading to cycloidal trajectories in the plane of the electron's motion?
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1What is the direction of the field at the position of the electron? – G. Smith Mar 03 '20 at 04:29
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Good question! At the position of the electron, the Biot-Savart law would imply that the magnetic field does not exist, so that the crossed electro-magnetic field does not exist in the circular path of the electron, thus making the question ill-posed. However, the crossed electro-magnetic field will exist in other atoms with multiple electrons in orbit. – kbakshi314 Mar 03 '20 at 04:37
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1@kb314 that is why quantum mechanics was needed. to get rid of orbits among other things – anna v Mar 03 '20 at 06:34