Charge distribution on concentric spheres

• Abhimessi10
In summary, two thin conducting spherical shells with radii R1 and R2, with the outer shell charged to q and the inner shell grounded, will result in a charge appearing on both shells. The charge on the inner shell cannot be assumed to be zero, as it is connected to ground. To approach this problem, one can think of a capacitor and a battery connected in parallel, with the bottom connection for both grounded to Earth. The potential on the surface of a shell with charge q is KQ/R and the potential at the centre is KQ/R. Adding an uncharged shell inside the first one will not change the potential at the centre, and if the inner shell is grounded, the potential can be equated to 0
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.

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?

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

Abhimessi10 said:
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?

Abhimessi10 said:
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?

berkeman said:
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?

berkeman said:
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:
Abhimessi10 said:
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?

haruspex said:
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?

Abhimessi10 said:
KQ/R right?
Right.
So now put another shell inside that has no charge. How will that change potential at the centre?

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

Abhimessi10 said:
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
haruspex said:
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?

Abhimessi10 said:
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?

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

Abhimessi10 said:
KQ'/R1+kQ/R2 ?
Right.
And if the inner shell is grounded what can you say about that potential?

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

Abhimessi10 said:
Equating potential of inner shell to 0?
Yes. So what equation do you get?

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

Abhimessi10 said:
Kq'/r1+kq/r2=0?
Right.

1. How does the charge distribution on concentric spheres affect the electric field?

The charge distribution on concentric spheres affects the electric field by creating a radial electric field that is directed from the outer sphere to the inner sphere. This electric field is stronger near the smaller sphere due to the higher concentration of charge.

2. How does the charge distribution change if the concentric spheres are made of different materials?

The charge distribution on concentric spheres will be affected by the material of the spheres because different materials have different abilities to conduct or hold charge. For example, if the outer sphere is made of a conductor, the charge distribution will be more evenly spread out compared to if it was made of an insulator.

3. Can the charge distribution on concentric spheres be affected by an external electric field?

Yes, an external electric field can influence the charge distribution on concentric spheres. If the external electric field is strong enough, it can cause the charges on the spheres to redistribute, leading to a change in the overall charge distribution on the spheres.

4. How does the distance between the concentric spheres affect the charge distribution?

The distance between the concentric spheres plays a significant role in the charge distribution. The closer the spheres are to each other, the stronger the electric field will be between them, resulting in a higher concentration of charge on the inner sphere.

5. Can the charge distribution on concentric spheres be used to determine the capacitance of the system?

Yes, the charge distribution on concentric spheres can be used to determine the capacitance of the system. The capacitance is directly proportional to the amount of charge and inversely proportional to the distance between the spheres. Therefore, by measuring the charge and distance, the capacitance of the system can be calculated.

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