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 :

Options

A. `V`
B. `2V`
C. `4V`
D. `-2V`

Answer

1

Explanation

`r`: radius of solid conducting sphere
`R`: radius of hollow spherical shell
`V_(A) - V_(B) = (1)/(4 pi in_(0)) [ ((Q)/(r )) - ((Q)/(R ))] = V`

`V'_(A) - V'_(B) = (1)/(4 pi in_(0)) [ { (Q)/(r ) + (-3Q)/(R )} - { (Q)/(R ) + (-3Q)/(R )}] = V`