`10^(-9)C` of charge is distributed over two concentric hollow spheres of radii 1cm and 2cm such that surface densities of charges are equal. Find the potential at their common centre.

Explanation

Given, `q_(1)+ q_(2)= 10^(-9)C`,
`r_(1)=1cm and r_(2)= 2cm`
`because sigma_(1) = sigma_(2)`
`(q_(1))/(4pi r_(1)^(2))= (q_(2))/(4pi r_(2)^(2)) rArr (q_(1))/(q_(2)) = (r_(1)^(2))/(r_(2)^(2)) = (1)/(4) rArr 4q_(1)= q_(2)`
`therefore V_(B)- V_(B)= (1)/(4pi epsi_(0)) ((q_(1))/(r_(1))- (q_(2))/(r_(2)))`
Substituting the values, we get V= 540V