Hi there. I'm new to PF, so please correct me on any mistakes in presenting my question. I'm just hoping to get some direction in doing this problem right.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Concentric spherical shells of radius a and b, with b > a, carry charge Q and -Q, repsectively, each charge uniformly distributed. Find the energy stored in the electric field of this system.

(From Purcell, Electricity and Magnetism, 2nd Ed. [I hate this book :yuck:])

2. Relevant equations

From Gauss's Law (for a sphere)

E= [tex] Q/r^2 [/tex]

U = [tex] \frac{1}{8\pi} \int_{Entire field} E^2 dv[/tex]

3. The attempt at a solution

I know I just have to sum up the E field and integrate over the volume of the entire sphere (or rather wherever the field is non-zero?) and that the E field will end up being a constant (or am I completely wrong?)

E inside inner sphere = 0 (field is zero inside spherical shell of charge)

E outside inner sphere = [tex]Q/(a^2)[/tex]

E inside outer sphere = [tex]-Q/b^2 + Q/a^2[/tex] (This one is the one I'm really unsure on)

E outside outer sphere = 0 (total charge is [tex]Q+(-Q) = 0[/tex])

And then do I integrate the E field squared in spherical coordinates from a to b? (As I end up with it as a constant I feel like I'm doing something wrong.)

Any help is greatly appreciated (I'm awful at E&M).

edit: Forgot to mention this is all in cgs units, not mks/si.

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# Homework Help: Gauss's Law/Energy Problem with Concentric Spheres

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