# Coloumb torque on a charge sphere?

1. Nov 10, 2011

### center o bass

I'm trying to explore a classical model of the hydrogen atom and here I find that the electrons spin will be conserved if we the external torque about it's center of mass is zero. I'm trying to prove to myself that indeed it is, but then I have to show that

$$\sum_i \vec r_i' \times \vec F_i = 0 .$$

Where $$\vec r_i'$$ is the vector from the center of mass to the i'th charge element dq of the sphere and $$\vec F_i$$ is the force on proton. I'm assuming that the electron is a uniformly charged sphere and not a point particle. Does anyone know how to show this or know a link to somewhere the calculation has been done? I suspect an equivalent calculation has been done in relation to planetary motion.. torque on a planet due to another.