Wait A Magnetic Moment

Consider an elemental ring of radius  $r_{es}$  on a sphere,  an electron is spinning around this ring with an angular velocity,  $\omega$,

The current due to this is,

$I=q\cfrac{\omega}{2\pi}$

The magnetic moment as a result of this current in a particular direction,

$M=I\pi r^2_{es}cos(\theta)=q\cfrac{\omega}{2\pi}\pi r^2_{es}cos(\theta)$

$M=\cfrac { 1 }{ 2 } q\omega { r }^{ 2 }_{es}cos(\theta)$

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?