Calculating the magnetic field of the Proton in Spin-orbit Coupling in Hydrogen Atom

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-independent Perturbation Theory, Section: Spin -Orbit Coupling. I understood that the spin–orbit coupling in Hydrogen atom arises from the interaction between the electron’s spin magnetic moment, and the proton’s orbital magnetic field B. But I did not understand why He calculated the magnetic field of the proton (B) using the angular momentum of the electron (L)! Please see the attached pictures.

• What is the point of this excercise? Aug 14, 2021 at 9:16

The author is looking at the proton from the point of view of the electron. Thus the magnetic field calculated is due to the electron orbiting the proton$$^1$$.
$$^1$$ Classical paths are just that. i.e, classical orbits, when in reality, the electron "path" is more complicated than that.