# Thread: nonuniformly charged spherical surface

1. ## nonuniformly charged spherical surface

A sphere of radius a in free space is nonuniformly charged over its surface such that the charge density is given by ρs(θ) = ρs0 sin 2θ, where ρs0 is a constant and 0≤θ≤∏. Compute the total charge of the sphere.

So I know
ρs = dQ/dS

Integrating the surface charge density function will give me the charge Q. My question is how would you set up this integral?

∫ρs0 sin 2θ dS
integrating 0 to ∏

Or would this involve much more than that such as a triple integral?

Any help getting this set up would be great! Thanks!

2. ## Re: nonuniformly charged spherical surface

Since you are integrating over the surface, you should have a double integral. If you use spherical coordinates, one angle goes from 0 to $\displaystyle 2\pi$, the other goes from 0 to $\displaystyle \pi$, all the while the radius is constant.

The surface element for a constant radius is

$\displaystyle dS = r^2 \sin \theta d\theta d\phi$

Can you set up the integral now?

3. ## Re: nonuniformly charged spherical surface

Yes after integration I got the total charge Q=0 C.

Thanks for the help.