Electric Potential due to conducting sphere and conducting shell

[haruspex]

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:
- V_ii, the potential at the inner sphere due to the charges on it
- V_io, the potential at the inner sphere due to the charge on the outer shell
- V_oi, the potential at the outer shell due to the charges on the inner sphere
- V_oo, 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 V_io and V_oo?

 

[ehild]

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

 

[haruspex]

Vio=Voo

Right. What about my other question?

 

[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]

Thanks @ehild

 

[gracy]

Am I right in post #35?

 

[gracy]

Thanks @Satvik Pandey the "starter".

 

[haruspex]

Am I right in post #35?

Yes, but to write it out in full, potential difference = (V_oo+V_oi)-(V_io+V_ii)=V_oi-V_ii+V_oo-V_io=V_oi-V_ii