Charged Spherical Shell and Solid Sphere

Click For Summary

Homework Help Overview

The discussion revolves around comparing the charge of a charged spherical shell and a solid conducting sphere, both of radius R, that are said to be at maximum potential. Participants explore the implications of this scenario in the context of capacitance and charge distribution.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between charge, potential, and capacitance, questioning how to determine which object can hold more charge. There is an emphasis on the need to calculate capacitance for both the solid sphere and the spherical shell, with some participants expressing uncertainty about the capacitance of the shell.

Discussion Status

The discussion is active, with participants raising questions about the meaning of "maximum potential" and its implications for charge comparison. Some suggest that if both objects are at the same potential, their capacitance and charge might also be equal, while others seek clarification on the definitions and formulas involved.

Contextual Notes

There is confusion regarding the term "maximum potential," which is not clearly defined in the original problem. Participants are also exploring the assumptions about charge distribution on conductors and the nature of capacitance in this context.

andyrk
Messages
658
Reaction score
5
A spherical shell and a conducting sphere each of radius R are charged to maximum potential. Which of the two has more charge?

My attempt:
Since in a conductor, no charge can reside inside the conductor so all charge is on the surface of the conductor just like the spherical shell. Now : Potential(V)=KQ/R

K and R are same for both. They are charged to maximum potential. Means there is a limit to the amount of charge the spherical shell and the solid conducting sphere can possess. My question is how to determine who can possesses more charge? I think we need to calculate capacitance of a solid sphere and a spherical shell in this. We know the capacitance of an isolated spherical capacitor.But how to calculate the capacitance of a isolated spherical shell?? Please reply soon!
 
Last edited:
Physics news on Phys.org
Anybody there?
 
What is the maximum potential you are talking about?
 
That is not mentioned in the question.
 
Well, this is rather strange. However, your observation that all the charge on a conducting sphere is at its surface is correct. Then, can the potential of the sphere be different from the potential of the shell, charges being equal?
 
voko said:
Well, this is rather strange. However, your observation that all the charge on a conducting sphere is at its surface is correct. Then, can the potential of the sphere be different from the potential of the shell, charges being equal?

No it can't be. But in the problem it says, which has greater charge. For this I think we need capacitance C for both the bodies. Like for the solid sphere C=4∏εoR

I don't think I have ever heard of capacitance of an isolated spherical shell. If we somehow get that and compare both of them, the one which is greater can be said to have the capacity to have more charge on it. But this is where I got stuck. There isn't any formula for the capacitance of a spherical shell. So if I can't do it this way then is there any other possible way to do this problem?
 
Capacitance is defined via charge and potential. If charges are equal, and potentials are equal, too, there is no other option for capacitance.
 
voko said:
Capacitance is defined via charge and potential. If charges are equal, and potentials are equal, too, there is no other option for capacitance.

No! Its not necessary that capacitance always involves charge and potential!
http://ta.ramk.fi/~jouko.teeriaho/capac.pdf
 
andyrk said:
No! Its not necessary that capacitance always involves charge and potential!
http://ta.ramk.fi/~jouko.teeriaho/capac.pdf

Capacitance is defined via charge and potential, just like the second slide at your link indicates.
 
  • #10
andyrk said:
No it can't be. But in the problem it says, which has greater charge. For this I think we need capacitance C for both the bodies. Like for the solid sphere C=4∏εoR

I don't think I have ever heard of capacitance of an isolated spherical shell. If we somehow get that and compare both of them, the one which is greater can be said to have the capacity to have more charge on it. But this is where I got stuck. There isn't any formula for the capacitance of a spherical shell. So if I can't do it this way then is there any other possible way to do this problem?
OK, so they are both kept at the same potential. And they ask 'which has greater capacitance?' So this is equivalent to 'which has stored greater charge?' right? (since we know C=Q/V). So now, you can either calculate the charge stored, or if you know the capacitance, then just use that.

hint: you can sort of figure out the answer logically. But you could also go through the calculation.
 
  • #11
BruceW said:
OK, so they are both kept at the same potential. And they ask 'which has greater capacitance?' So this is equivalent to 'which has stored greater charge?' right? (since we know C=Q/V). So now, you can either calculate the charge stored, or if you know the capacitance, then just use that.

hint: you can sort of figure out the answer logically. But you could also go through the calculation.

I am not able to sort it out. Tried to think a lot. Could you help?
 
  • #12
start by thinking the isolated sphere has charge Q1 and the isolated shell has charge Q2. (which may or may not be the same). Now in both situations, where are the charges, and what is the form of the potential in both situations? From this, what would you say about Q1 and Q2?
 
  • #13
See, they are charged to maximum potential, which we do not know the value of. So we can't say which is greater, Q1 or Q2.?
 
  • #14
As voko pointed out, the term 'maximum potential' is weird. If you don't know what it means you should inquire of your lecturer or whoever as to its meaning. We at PF are telling you it's meaningless in the context of the remainder of the question.

We shall assume it means the potential of the sphere and the shell are the same. It doesn't matter how high the potential is.

One can visualize the meaning of 'capacitance' of an isolated sphere or shell as a capacitor formed by the sphere or inner shell of radius a and an outer shell of infinite radius b. So, as you know, the capacitance of such a system is (1/k)(1/a - 1/b) with k = 1/(4 pi epsilon-sub-zero). For b = infinity we get C = a/k.

So if V is the same for both capacitors (sphere plus infinite outer shell vs. inner shell plus infinite outer shell), then the capacitance is the same and since Q = CV it follows immediately that Q is the same for both capacitors also.
 
  • #15
No..it is not 2 concentric spherical shells. Its an isolated solid sphere and an isolated spherical shell of the same radius R which are charged to the maximum potential. THe formula of capacitance you wrote is of two concentric spherical shells of radii a and b (a>b)..
 
  • #16
andyrk said:
No..it is not 2 concentric spherical shells. Its an isolated solid sphere and an isolated spherical shell of the same radius R which are charged to the maximum potential. THe formula of capacitance you wrote is of two concentric spherical shells of radii a and b (a>b)..

Ah, thank you, I know. What I said was one can visualize a capacitor formed by a sphere of radius a and an outer concentric shell of radius b = infinity.

Or, an inner shell of radius a and again an outer shell of radius b = infinity.

Believe me, it works.
 
  • #17
rude man said:
Ah, thank you, I know. What I said was one can visualize a capacitor formed by a sphere of radius a and an outer concentric shell of radius b = infinity.

Or, an inner shell of radius a and again an outer shell of radius b = infinity.

Believe me, it works.

Oh yes. Thanks. It really works :)
 

Similar threads

Electric potential due to shell containing a charge at an offset outside
  • · Replies 5 ·
Replies
5
Views
1K
Force between point charges at the center of two spherical shells
  • · Replies 4 ·
Replies
4
Views
2K
The energy needed to construct a charged hollow spherical shell with finite thickness
  • · Replies 1 ·
Replies
1
Views
945
Spherical conducting shell enclosing a non-conducting core
  • · Replies 5 ·
Replies
5
Views
749
Flux through a cylindrical surface enclosing part of a sphere
  • · Replies 9 ·
Replies
9
Views
2K
Charged sphere and charged conducting shell
  • · Replies 9 ·
Replies
9
Views
3K
How Does a Dielectric Influence Charge Induction on a Conducting Shell?
  • · Replies 1 ·
Replies
1
Views
2K
Potential energy of a sphere in the field of itself
  • · Replies 43 ·
2
Replies
43
Views
4K
How Does Charging a Conducting Shell Affect Potential Difference?
  • · Replies 7 ·
Replies
7
Views
2K
Spherical conductor shell problem
  • · Replies 19 ·
Replies
19
Views
4K