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Homework Statement:

What is the energy configuration of a system consisting of two concentric shell?
The internal shell has radius a and charge q
The external shell radius b and charge q
Relevant Equations:
 All below
I found the total work done is:
##\frac{q^2}{8\pi \varepsilon a} + \frac{q^2}{8\pi \varepsilon b} + \epsilon \int E_{1}.E_{2} dv##
The third is a little troublesome i think, but i separated into threeregions, inside the "inside" shell, between both shell and outside both.
Inside => ##E_{1}.E_{2} = 0##
Between => ##E_{1}.0 = 0##
Outside => ##\epsilon \frac{(4\pi (kq)^2)}{b}## = ##\frac{(q)^2}{4\pi \epsilon b}##
so
##\frac{3q^2}{8\pi \epsilon b} + \frac{q^2}{8\pi \varepsilon a}##
is this right?
##\frac{q^2}{8\pi \varepsilon a} + \frac{q^2}{8\pi \varepsilon b} + \epsilon \int E_{1}.E_{2} dv##
The third is a little troublesome i think, but i separated into threeregions, inside the "inside" shell, between both shell and outside both.
Inside => ##E_{1}.E_{2} = 0##
Between => ##E_{1}.0 = 0##
Outside => ##\epsilon \frac{(4\pi (kq)^2)}{b}## = ##\frac{(q)^2}{4\pi \epsilon b}##
so
##\frac{3q^2}{8\pi \epsilon b} + \frac{q^2}{8\pi \varepsilon a}##
is this right?
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