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!