Charge distribution on concentric spheres

[Abhimessi10]

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 doesn't involve any connection?

 

[Orodruin]

The inner shell is connected to ground so you cannot make the assumption that the charge on it is zero.

 

[Abhimessi10]

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]

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?

 

[Abhimessi10]

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.

 

[haruspex]

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?

 

[Abhimessi10]

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]

KQ/R right?

Right.
So now put another shell inside that has no charge. How will that change potential at the centre?

 

[Abhimessi10]

Right.
So now put another shell inside that has no charge. How will that change potential at the centre?

It will not change?

 

[haruspex]

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?

 

[Abhimessi10]

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]

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?

 

[Abhimessi10]

Suppose it has charge q'. What is the potential at the centre now?

KQ'/R1+kQ/R2 ?

 

[haruspex]

KQ'/R1+kQ/R2 ?

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

 

[Abhimessi10]

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

Equating potential of inner shell to 0?

 

[haruspex]

Equating potential of inner shell to 0?

Yes. So what equation do you get?

 

[Abhimessi10]

Yes. So what equation do you get?

Kq'/r1+kq/r2=0?

 

[haruspex]

Kq'/r1+kq/r2=0?

Right.