.

A proton (charge $+e$) with mass $m_p$ is in a circular orbit of radius $r$ such that it has an angular momentum given by $\vec{L}$. The orbiting proton has a magnetic moment $\vec{m}$ parallel to its angular momentum. When the orbiting proton is placed in a uniform magnetic field of strength $B$ so that $\vec{L}$ makes an angle of $\theta$ with $\vec{B}$, the angular momentum precesses around $\vec{B}$. Find:

a) The magnetic moment of the orbit in terms of $\vec{L}$;

b) The angular frequency with which the angular momentum precesses.