The current due to this is,
\(I=q\cfrac{\omega}{2\pi}\)
\(M=I\pi r^2_{es}cos(\theta)=q\cfrac{\omega}{2\pi}\pi r^2_{es}cos(\theta)\)
\(M=\cfrac { 1 }{ 2 } q\omega { r }^{ 2 }_{es}cos(\theta)\)
Now we consider the summation of all such moments confined to a sphere of radius \(r_{es}\), up to \(\theta=\cfrac{\pi}{2}\)
\(s_e=\int^\frac{\pi}{2}_0{\frac { 1 }{ 2 } q\omega r^2_{es}cos(\theta)}dr\)
\(s_e=\frac { 1 }{ 2 } q\omega r^2_{es}\int^\frac{\pi}{2}_0{cos(\theta)}dr\)
\(s_e=\frac { 1 }{ 2 } q\omega r^2_{es}\)
And so, the spin of an electron is,
\(S_e=2s_e=q\omega r^2_{es}\)
At light speed,
\(S_e=qc r_{es}\)
And given \(n\) valence electrons,
\(S_e=2ns_e=nq\omega r^2_{es}\)
This is not true, the effects of more than one orbiting electrons are not likely to sum simply. In fact less than n times.
It does sum simply! The electrons are ATTRACTED to one another because of the B field they create, like two parallel current carrying wire. The electron orbit in parallel and their magnetic moment sum numerically.
At light speed,
\(S_e=nqc r_{es}\)
Which is very interesting, provided \(e=e_s4\pi r^2_{es}\) when \(r\rightarrow0\). So, why and how would a magnetic moment change?
