# Electric Potential due to conducting sphere and conducting shell

#### ehild

Homework Helper
I have found the answer of this question in a google book as
ANSWER: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

that the answer mentions the potential difference between solid sphere and hollow shell
but the question asks potential difference between
surface of the solid sphere and that of the outer surface of the hollow shell
Are both same?
Are they conductors? What do you know the potential of a conducting body? inside, outside any point?

Homework Helper

#### gracy

What do you know the potential of a conducting body?
It is same everywhere inside the conductor and on surface of conductor.

#### ehild

Homework Helper
It is same everywhere inside the conductor and on surface of conductor.
So is the potential difference not the same between the solid sphere and shell as the potential difference between the surface of the solid sphere and the outer surface of the shell?

#### gracy

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?

#### haruspex

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Gold Member
2018 Award
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?

#### ehild

Homework Helper
Remember Gauss' Law. Does the electric field depend between the solid sphere and the shell on the charge of the shell?

#### gracy

What do you know about the relationship directly between Vio and Voo?
Vio=Voo

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#### gracy

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

#### gracy

Am I right in post #35?

#### haruspex

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Gold Member
2018 Award
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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