First let's just think about it classically, ignoring quantum mechanics. The nucleus is heavy and positively charged. The electron is light and negatively charged. They attract, so if the electron moves sideways at the right speed it will bend toward the nucleus and just keep on bending in a circle, the same as a satellite orbiting earth. Or if it's at some other speed, it will make an elliptical orbit, or in the extreme case of no initial speed, it will just fall straight in on a radial trajectory. Quantum mechanically, things are harder to visualize. You can think about the hydrogen ground state for example as an electron simultaneously oscillating in and out radially along all possible directions. (No one can stop you from thinking it!) And for some particular electron energy, all of these paths add up constructively, because of the wave nature of the electron.

So, I think the best answer to your question is that there are states in which the electron can be thought of as orbiting the nucleus (states with nonzero angular momentum), but in the ground state, where a typical hydrogen atom spends most of its time, there's no angular momentum, hence no orbiting.


That's just the way nature acts. Perhaps the question should be: How does physics model a moving charge sourcing a magnetic field? This is a straightforward application of the Lorentz transform, as follows.

Consider a charge which is not accelerating. There is some frame in which the charge is at rest. In that frame, there is only an electric field (which you can find from electrostatics).

In every inertial frame other than that frame, there will be a magnetic field, because of how electric and magnetic fields transform under change of frame:
E⃗′∥=E⃗∥
E⃗′⊥=γ(E⃗⊥+v⃗×B⃗)
B⃗′∥=B⃗∥
B⃗′⊥=γ(B⃗⊥−v⃗×E⃗)
whereγ=(1−v2)−1/2is the Lorentz factor and here and abovec=1. It should be clear that the magnetic field in the new (primed) frame is nonzero, perpendicular to the direction of the velocity of the frame (with respect to the 'rest' frame; this is minus the particle velocity in the new frame).

This type of magnetic field is simply the result of special relativity on electric charges. However, not all magnetic fields are the result of moving charges. Specifically, spin creates a magnetic field, even when charges are not in motion.

PS The transformation law above looks simpler in tensor notation. The electric and magnetic fields are both part of the antisymmetric 'Maxwell tensor' (better a 2-form),Fab. The transformation law forFis
F′ab=ΛcaFcdΛdb
whereΛcais the Lorentz transformation matrix