(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given

[tex]V(r)=\frac{Q}{4\pi \epsilon_0}\frac{1}{r+a},[/tex]

find the total charge.

2. Relevant equations

[tex]\overline{E}=-\nabla V[/tex]

[tex]\rho=\epsilon_0 \nabla \cdot \overline{E} [/tex]

[tex]\rho=-\epsilon_0 \nabla^2 V[/tex]

3. The attempt at a solution

I started out by finding the charge density [tex]\rho[/tex] from [tex]\overline{E}[/tex], and I got the result:

[tex]\rho(r)=\frac{aQ}{2\pi r(a+r)^3}[/tex]

I might as well have gone with Poisson's equation to start with, but I didn't think of that.

I have, however, no idea how to proceed from here to find the TOTAL charge. I'm assuming I somehow have to integrate over some region (all of space?), but I don't know how to do it. Any pointers at setting up the integral would be appreciated. I should be able to handle it from there.

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# Homework Help: Total charge given potential V(r)

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