Electric Potential due to conducting sphere and conducting shell

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Homework Help Overview

The discussion revolves around the electric potential difference between a solid conducting sphere with charge Q and a concentric conducting hollow spherical shell, initially uncharged. The problem explores how the potential difference changes when the shell is given a charge of -3Q.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss the potential induced on the surfaces of the sphere and shell, referencing Gauss' Law to understand the electric field and potential difference. There are attempts to calculate the net potential at the surfaces and questions about the implications of changing the shell's charge.

Discussion Status

Participants are actively exploring the implications of charge distribution on the sphere and shell, with some guidance provided on integrating electric fields to find potential differences. There is an ongoing examination of the assumptions regarding charge sharing and the behavior of electric fields in this context.

Contextual Notes

There are discussions about the potential being the same on both surfaces of the conducting shell and the implications of adding charge to the shell. Participants express uncertainty about the effects of these changes on the electric field and potential calculations.

  • #31
gracy said:
Because the potential difference between solid sphere and hollow shell depends on the radii of two spheres and charge on the inner sphere.Since the two values have not changed therefore potential difference does not change.

I want to ask why does potential difference only depend on charge on the inner sphere and not on charge on the shell?
The potential at a point is the sum of the potentials due to all the charges in the system. So we can think about:
- Vii, the potential at the inner sphere due to the charges on it
- Vio, the potential at the inner sphere due to the charge on the outer shell
- Voi, the potential at the outer shell due to the charges on the inner sphere
- Voo, the potential at the outer shell due to the charge on the outer shell
In terms of these, what is the potential difference between the inner sphere and outer shell?
What do you know about the relationship directly between Vio and Voo?
 
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  • #32
Remember Gauss' Law. Does the electric field depend between the solid sphere and the shell on the charge of the shell?
 
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  • #33
haruspex said:
What do you know about the relationship directly between Vio and Voo?
Vio=Voo
 
  • #34
gracy said:
Vio=Voo
Right. What about my other question?
 
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  • #35
haruspex said:
what is the potential difference between the inner sphere and outer shell?
Vii-Voi
Now I can see why potential difference only depends on charge on the inner sphere and not on outer shell.Thanks haru:smile::smile:
 
  • #36
  • #37
Am I right in post #35?
 
  • #38
  • #39
gracy said:
Am I right in post #35?
Yes, but to write it out in full, potential difference = (Voo+Voi)-(Vio+Vii)=Voi-Vii+Voo-Vio=Voi-Vii
 
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