# B Charge distribution in shells

1. Nov 22, 2015

### gracy

I don't understand charge distribution properly.
Here is what I found somewhere
Figure (1)shows three concentric thin spherical shells A,B and C of radii a,b and c respectively.The shells A and C are given charges q and -q respectively and the shell B is earthed.Find the charge appearing on the surfaces of B and C.
Figure (2) shows how charge distribution would take place.

Charge distribution:The inner surface of B must have a charge -q from the Gauss's law.Suppose,the outer surface of B has a charge q'.The inner surface of C must have a charge -q' from the Gauss's law.As the net charge on C must be -q ,it's outer surface should have a charge q'-q.The charge distribution is shown in the figure.

But as per my understanding
The inner surface of B must have a charge -q so that net charge becomes zero because as shell B is earthed it has to be at zero potential.But then we will be violating "conservation of charge"law.As originally shell B does not have any charge.That's why the outer surface of B should have charge q.
I am all confused about shell C.As according to Gauss's law it is ok to have charge q on the outer surface(i.e inside shell C) of B because this gives net charge q inside shell C and that was the case initially.But then total charge of shell C becomes zero and that violates "conservation of charge"law.

Last edited: Nov 22, 2015
2. Nov 22, 2015

### Staff: Mentor

Shell B is not isolated since it is connected to ground. Ground can be treated like a big neutral sea of available charges (positive or negative). If they can (if there's a conductive path) they will move to try to cancel charges and their fields.

So the charge conservation rule doesn't hold for shell B since it can draw on charges through its ground connection.

Did the problem source determine a value for the charge q' ?

3. Nov 22, 2015

### gracy

How can we determine if any shell is isolated?

4. Nov 22, 2015

### gracy

No.

5. Nov 22, 2015

### Staff: Mentor

A body is isolated if it has no external connections that can conduct charges, that is, charges cannot leave or exit the object. Shell B is not isolated because it has a connection to ground by which charges can move onto or off of the shell.

6. Nov 22, 2015

### gracy

Can charge conservation be applied to shell C,I think yes.Because it seems isolated.

7. Nov 22, 2015

### Staff: Mentor

Yes. Both shells A and C are isolated so charge conservation holds for them.

8. Nov 22, 2015

### gracy

9. Nov 22, 2015

### Staff: Mentor

There can be no electric field inside a conductor, so something must prevent any field originating in the interior of shell C from penetrating shell C's material. If shell B has some charge q' on its surface, then that charge will attract its opposite charge -q' to the inner surface of C, satisfying the requirement of cancelling the field from B. That charge of -q must have come from the total charge q on the C shell (the C shell being isolated), leaving charge q-q' to present at the outer surface of C.

10. Nov 22, 2015

### gracy

But according to @nasu

11. Nov 22, 2015

### Staff: Mentor

I believe that @nasu was referring to the field inside the cavity, not inside the shell conductor.

12. Nov 22, 2015

### gracy

13. Nov 22, 2015

### gracy

Did you mean shell C by shell conductor?

14. Nov 22, 2015

### gracy

But he did not mention cavity anywhere?Did he mean If you put charge inside the cavity of conducting shell,the field does not have to be zero.

15. Nov 22, 2015

### Staff: Mentor

Yes. If you put a charge in the cavity there will be a field in the cavity due to that charge.

16. Nov 22, 2015

### gracy

17. Nov 22, 2015

### Staff: Mentor

I wanted to distinguish the shell itself from the cavity that the shell surrounds. By shell conductor I mean the conductive material of the shell itself.

18. Nov 22, 2015

### gracy

If any conductive shell surrounds a hollow conductor,can that hollow conductor be treated as a cavity inside the conductive shell?

19. Nov 22, 2015

### gracy

But the field would be zero inside the conductor surrounding that cavity?

20. Nov 22, 2015

### Staff: Mentor

I'm not sure that I understand what you're getting at. As far as I can tell you're describing nested conductive shells, or several hollow objects inside another shell. As you've seen, charges on nested shells can influence the field external to the outer shell. Any fields in the interior of that outer shell will be due to charges in its cavity, and they can interact between each other the way charges usually do. These charges can reside on hollow conductors.

Can you draw a scenario that might make your query more clear??