Electric Potential due to conducting sphere and conducting shell.

1. The problem statement, all variables and given/known data
A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of – 3Q, the new potential difference between the same two surfaces is????
Answer is V.Let R be the radius of the outer surface of shell and r of inner surface and let the radius of sphere be X.
Consider epsilon not as ‘ε’

2. Relevant equations
potential at a point =Q/4∏ε.

3. The attempt at a solution
If Q charge is on the surface of sphere then it will induce -Q charge on the inner surface of the shell and Q on the outer surface of shell.Potential at the surface of sphere due to charge inside sphere is Q/4∏εX but I am unable to calculate NET potential at surface of sphere(potential due to charge outside and inside sphere).
I know that potential on the outer surface of shell is Q/4∏εR.


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