# Charge distribution on concentric spheres

## 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.

## 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?

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.

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?

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?

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?

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?
Still i think its 0 .Sorry i was born dumb.

Last edited:
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?

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?

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?

Right.
So now put another shell inside that has no charge. How will that change potential at the centre?
It will not change?

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?

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?

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?

Suppose it has charge q'. What is the potential at the centre now?
KQ'/R1+kQ/R2 ?

haruspex
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KQ'/R1+kQ/R2 ?
Right.
And if the inner shell is grounded what can you say about that potential?

Right.
And if the inner shell is grounded what can you say about that potential?
Equating potential of inner shell to 0?

haruspex
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Equating potential of inner shell to 0?
Yes. So what equation do you get?

Yes. So what equation do you get?
Kq'/r1+kq/r2=0?

haruspex