# why electron moves arround nucleus?whyamoving charge creat magnetic field ? give answer

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why electron moves arround nucleus?whyamoving charge creat magnetic field ? give answer

## 1 Answers

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