Electrostatics - Finding amount of heat in a circuit

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SUMMARY

The discussion focuses on calculating the amount of heat produced in a circuit involving a solid conducting sphere and a concentric conducting spherical shell. The user initially calculated the potential energy difference as kq²/2a but later found the correct answer to be kq²/4a. The potential energy before closing the switch was determined to be 5kq²/6a, while after closing the switch, it was kq²/3a. The discrepancy in the heat calculation is the central issue addressed in the forum.

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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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