- #36
ehild
Homework Helper
- 15,542
- 1,917
What is the potential of the outer surface then if the shell is very thin? infinite?gracy said:Distance between inner and outer surfaces of shell is "a "
What is the potential of the outer surface then if the shell is very thin? infinite?gracy said:Distance between inner and outer surfaces of shell is "a "
Please, read my post.gracy said:Thin or infinite?which one?
0.0001 multiplied by R?ehild said:0.0001R
@gracy ,ehild said:What is the potential of a sphere of radius R and charge Q at distance 0.0001R from its surface?
R is not very big number right?SammyS said:This is asking,"What is the potential due to a (conducting) sphere of radius R and charge Q evaluated at distance 0.0001R from its surface?
##\frac{KQ}{R}##SammyS said:What is the potential due to a (conducting) sphere of radius R and charge Q evaluated at distance 0.0001R from its surface?
R may be any (positive) number.gracy said:R is not very big number right?
That's the potential at a location just inside the sphere, at a distance 0.9999R from sphere's center. Perhaps that is what ehild was asking for.gracy said:##\displaystyle \frac{KQ}{R}##
"gracy said:Ok.There is a question.
A solid conducting sphere of radius, a, having a charge, Q, is surrounded by a neutral conducting shell of inner radius, 2a, and outer radius, 3a, as shown.Find the amount of heat produced when a switch connecting the spheres is closed.
I'm assuming that the region between r = 2a and r = 3a is the outer conducting shell.gracy said:
What about induced charges ?@Tsny asked me to consider the induced charges as wellSammyS said:The potential at the outer surface of the shell is given by Vouter=kQ3a Vouter=kQ3a \displaystyle \ V_\text{outer}=k\frac{Q}{3a} \ , assuming that potential → 0 as r → ∞ .
That's what I have done inTSny said:Use this along with the principle of superposition to find the potential at any point in your problem. You have 3 spherical charge distributions and the potential at any point is the sum of the potentials created by each individual spherical charge distribution.
I think it should be ##\frac{-KQ}{3a}##(using shell theorem)ehild said:why is the potential due to the charge on the inner surface of the shell -KQ/a on the outer surface?
gracy said:I think it should be ##\frac{-KQ}{3a}##(using shell theorem)
Yes, good. It's the potential on the outer surface of the shell due to the charge on the inner surface.gracy said:##\frac{-KQ}{3a}## it will be potential of outer shell due to charge on inner surface of outer shell .
##\frac{KQ}{3a}##TSny said:What is the total potential on the outer surface of the shell due to all 3 charge distributions?
TSny said: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?
Your work looks correct.gracy said:The answer I got is indeed a correct answer.
The switch makes a connection from the solid sphere to the shell.ehild said: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?
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?SammyS said:The switch makes a connection from the solid sphere to the shell.
Had to be the latter.ehild said: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).ehild said: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?