# Electrostatics - finding the total charge of a sphere with varying charge density

by iejedijuerijr
Tags: charge, density, electrostatics, sphere, varying
 P: 1 1. The problem statement, all variables and given/known data I was given a sphere with radius R and a charge density function δ(r),where r is the distance from the center of the sphere. I want to find the total charge in the sphere. 2. Relevant equations I know that Q = δV 3. The attempt at a solution I tried integrating V ∫δ(r)dr over 0 to R, but I'm not sure that will give me the total charge, but am unsure that's the right way to go about this. is it? thanks.
 P: 175 I believe your approach is correct. Just remember that when integrating from 0 to R in spherical coordinates your must remember to use the factors associated with this change of variable. That is, I think you will want to integrate: Q = $\int^{2\pi}_{0}$ $\int^{\pi}_{0}$ $\int^{R}_{0}$ $\delta$(r) r$^{2}$ sin$\theta$ dr d$\theta$ d$\phi$ where Q is the total charge enclosed by the sphere and R is the radius of the sphere.

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