Electric Potentials: concentric spheres

[vsage]

Two concentric spheres of radii 1.65 cm and 19.0 cm, respectively, are given equal but opposite charges of 6.35e-08 C. How much energy is stored in the system (in J)?

I know V = U/q where U would be the entire energy stored in the system beacuse it's not in motion. I know q's but I just don't know how to apply it.

I've thought about this so much. I tried setting up a ridiculous integral for solving this but it just went way over my head. The question doesn't really even make sense because wouldn't some of the charges overlap each other? I think the teacher meant hollow spheres. A little point in the right direction, please. (Test tomorrow) :)

 

[Tide]

I think the problem is about spherical shells.

I'm curious - has your class discussed the capacitance of a spherical capacitor? If so then you may already have a formula for finding the energy stored. If not, nevermind! :-)

 

[vsage]

Yes the teacher touched on it for the last half of a lecture I think but it wasn't much more than parallel plates (a lecture is 2.5 hours though so that's a lot of time). Oh yeah I see it may be addressed in the chapter he touched on. Thanks tide I'll see if I can't work something out from this.

Ah, found it.

the potential difference between the spheres

q/(4*pi*enot) * (outer radius - inner radius) / (outer radius * inner radius)

I wish I had enough time to derive this formula but I'm in a crunch :\

My grasp of this subject is worse than I'd like it to be but since dV = dU/q ,
the total energy is dV * q? Am I correct?

Edit: The computer that checks my answers says I was wrong.. I got 4.98e11 joules

 

[vsage]

Can my answer be confirmed? The computer keeps telling me I'm wrong argh. Ok now I'm getting 2e-03 joules which I know has to be wrong as well. This is so confusing sigh. Edit ok here my work:

C = q^2 / U

C = 4*pi*enot * (Ro * Ri) / (Ro - Ri)

where enot is 8.85e-12 and Ro is the outer radius and Ri is the inner radius

C = (6.35e-08)^2 / U = 2.01e-12

U = (6.35e-08)^2 / 2.01e-12

= 2.01e-03

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