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

  • #1

Homework Statement



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.


Homework Equations



I know that Q = δV


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.
 

Answers and Replies

  • #2
215
11
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 = [itex]\int^{2\pi}_{0}[/itex] [itex]\int^{\pi}_{0}[/itex] [itex]\int^{R}_{0}[/itex] [itex]\delta[/itex](r) r[itex]^{2}[/itex] sin[itex]\theta[/itex] dr d[itex]\theta[/itex] d[itex]\phi[/itex]

where Q is the total charge enclosed by the sphere and R is the radius of the sphere.
 

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