# Coloumb torque on a charge sphere?

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.

## Answers and Replies

kuruman
Science Advisor
Homework Helper
Gold Member
... and ##\vec F_i## is the force on proton.
Is this the standard Coulomb attraction force? Are you modeling the proton as a point charge? If the answer to both questions is "yes", the torque on ##dq## will be zero because ##\vec r'_i## is antiparallel to ##vec F'_i## which would make the cross product zero. If there is a "no" answer, please be more specific about your model. A separate question is what do you mean by spin? Are you imagining the electron as a charged "spinning" sphere?