# Potential energy in concentric shells

TSny
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I think it should be ##\frac{-KQ}{3a}##(using shell theorem)
This is correct for the potential created at the outer surface by the negative charge on the inner surface.

gracy
##\frac{-KQ}{3a}## it will be potential of outer shell due to charge on inner surface of outer shell .

TSny
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##\frac{-KQ}{3a}## it will be potential of outer shell due to charge on inner surface of outer shell .
Yes, good. It's the potential on the outer surface of the shell due to the charge on the inner surface.

gracy
TSny
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What is the total potential on the outer surface of the shell due to all 3 charge distributions?

Can you use the shell theorem to show that the total potential is the same at all points within the spherical shell material? (Of course this must be the case, since all points of a conductor are at the same potential in electrostatics.)

gracy
TSny
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As ehild pointed out, you made a mistake in the term that I have circled in blue below. From post #50, you now have the correct expression for this term. Everything else looks good to me.

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gracy
What is the total potential on the outer surface of the shell due to all 3 charge distributions?
##\frac{KQ}{3a}##

TSny
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OK. So, you find that the initial PE of the system is 5kQ2/(12 a).
[You left out the "a" in the denominator, but I know you meant it to be there.]

Why do you think this is wrong?

gracy
ehild
Homework Helper
OK. So, you find that the initial PE of the system is 5kQ2/(12 a).
[You left out the "a" in the denominator, but I know you meant it to be there.]

Why do you think this is wrong?
The question was "A solid conducting sphere of radius a having a charge Q is surrounded by a conducting shell of inner radius 2a and outer radius 3a as shown.Find the amount of heat produced when switch is closed."
Where is that switch?

gracy
Ok.It was initial energy .
To find the final potential energy we will have to consider final situation i.e after closing switch.
After closing switch entire charge i.e Q will be transferred to outer shell to equate the potentials of inner sphere and outer shell.

The answer I got is indeed a correct answer.Thank you so much @TSny @ehild and @SammyS

Last edited:
TSny
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gracy
SammyS
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The question was "A solid conducting sphere of radius a having a charge Q is surrounded by a conducting shell of inner radius 2a and outer radius 3a as shown.Find the amount of heat produced when switch is closed."
Where is that switch?
The switch makes a connection from the solid sphere to the shell.

gracy
ehild
Homework Helper
The switch makes a connection from the solid sphere to the shell.
Have you seen that switch anywhere in the thread, or you could see the original figure in Gracy's book due to your supernatural abilities?

TSny
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Have you seen that switch anywhere in the thread, or you could see the original figure in Gracy's book due to your supernatural abilities?

ehild
SammyS
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Have you seen that switch anywhere in the thread, or you could see the original figure in Gracy's book due to your supernatural abilities?
Not supernatural. (Thanks for the vote of confidence, TSny).

Back in Post #47, I suggested to gracy, that she edit the OP. In that suggestion, I added a few words to her restated problem as it appeared in Post #4.

I knew about the switch from a link to a video that gracy sent to me in a pm.

I should have pushed harder for her to give a more complete statement of the problem.
Here is a screen shot:

Here is the figure at a larger scale.

This video can be found on the site: physicsgalaxy.com , by Ashish Arora.

gracy