Electrostatics - Finding amount of heat in a circuit

AI Thread Summary
The discussion revolves around calculating the amount of heat produced in a circuit involving a solid conducting sphere and a concentric conducting spherical shell. The user attempts to find the heat generated by determining the difference in electrostatic potential energy before and after closing the switch. Initial calculations yield a heat value of kq²/2a, while the expected answer is kq²/4a. The user details the charge distribution and potential energy calculations for both states but is unsure about the discrepancy in their final answer. Clarification on the correct approach and any errors in their calculations is sought to resolve the issue.
Abhishekdas
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Homework Statement


A solid conducting sphere of radius 'a' having a charge q is surrounded by a concentric conducting sphereical shell of inner radius 2a and outer radius 3a (please refer diagram)...
Find the amount of heat produced when switch is closed ...


Homework Equations





The Attempt at a Solution


I proceeded by finding out the Potential energy(electrostatic) of the system initially and finally and their difference is equal to heat lost...Doing all the calculations i get kq2/2a as theanswer but answer is kq2/4a...
So can anyone try and tell me if my answer is correct or not...

I proceeded as below...
part 1.(before switch is closed)

charge distribution is q in the outer surface of smaller sphere, -q on the inner surface of shell and q on the outer surface of shell...PE of system at this stage is 5kq2/6a.

Part 2(after switch is closed)
charge distribution is 0 on the outer surface of smaller sphere and 0 also on the inner surface of shell and q on the outer surface of shell...
PE of system at this stage is kq2/3a

Difference between Pe = heat so answer is kq2/2a...
 

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Please can anyone point out if there is any error?
 

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