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Charge distribution on concentric spheres

  • #1

Homework Statement


Two thin conducting spherical shells have radii R1 and R2.Outer shell is charged to q and inner shell earthed.Find charge appearing on both the shells.

Homework Equations



The Attempt at a Solution


Isnt the charge on inner shell 0 and charge on outer shell remains Q as it doesnt involve any connection?
 

Answers and Replies

  • #2
Orodruin
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The inner shell is connected to ground so you cannot make the assumption that the charge on it is zero.
 
  • #3
So how do i approach this problem?
Sorry isn't the inner shell at potential zero as it is connected to the earth and thus holds 0 charge

If i am wrong please correct me and tell me how to do this?
 
  • #4
berkeman
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Sorry isn't the inner shell at potential zero as it is connected to the earth and thus holds 0 charge

If i am wrong please correct me and tell me how to do this?
Picture a capacitor and a battery connected in parallel, and the bottom connection for both is Earth grounded. What is the charge on each plate of the capacitor? :smile:
 
  • #5
Picture a capacitor and a battery connected in parallel, and the bottom connection for both is Earth grounded. What is the charge on each plate of the capacitor? :smile:
Picture a capacitor and a battery connected in parallel, and the bottom connection for both is Earth grounded. What is the charge on each plate of the capacitor? :smile:
Still i think its 0 .Sorry i was born dumb.
 
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  • #6
haruspex
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Still i think its 0 .Sorry i was born dumb.
Forget the inner shell for the moment. If you have a shell radius r with charge q, what is the potential on its surface? What is the potential at the centre of the shell?
 
  • #7
Forget the inner shell for the moment. If you have a shell radius r with charge q, what is the potential on its surface? What is the potential at the centre of the shell?
KQ/R right?
 
  • #8
haruspex
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KQ/R right?
Right.
So now put another shell inside that has no charge. How will that change potential at the centre?
 
  • #9
Right.
So now put another shell inside that has no charge. How will that change potential at the centre?
It will not change?
 
  • #10
haruspex
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It will not change?
And so cannot become zero.
Do you still think that a grounded sphere placed inside the shell would have no charge?
 
  • #11
Ok
And so cannot become zero.
Do you still think that a grounded sphere placed inside the shell would have no charge?
But how do i find charges when the inner shell is earthed?
 
  • #12
haruspex
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Ok

But how do i find charges when the inner shell is earthed?
Suppose it has charge q'. What is the potential at the centre now?
 
  • #13
Suppose it has charge q'. What is the potential at the centre now?
KQ'/R1+kQ/R2 ?
 
  • #14
haruspex
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KQ'/R1+kQ/R2 ?
Right.
And if the inner shell is grounded what can you say about that potential?
 
  • #15
Right.
And if the inner shell is grounded what can you say about that potential?
Equating potential of inner shell to 0?
 
  • #16
haruspex
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Equating potential of inner shell to 0?
Yes. So what equation do you get?
 
  • #17
  • #18
haruspex
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