A charge Q is distributed over two concentric hollow spheres of radii r and `R (gt r)` such that the surface charge densities are equal. Find the potential at the common centre.

Answer

2

Explanation

Let `q_(1) and q_(2)` be the charges on them
`sigma = sigma_(2)`
`therefore (q_(1))/(4 pi r^(2)) = (q_(2))/(4 pi R^(2)) " " therefore " " (q_(1))/(q(2)) = (r^(2))/(R^(2))`
i.e., charge on them is distributed in above ratio.
or `q_(1) = (r^(2))/(r^(2) + R) Q and q_(2) = (R^(2))/(r^(2) + R^(2)) Q`
Potential at centre V = potential due to potential due to `q_(2)`