A charge Q is distributed over two concentric conducting thin spherical shells radii r and R `(R gt 1)` . If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

Answer

`(Q(R+r))/(4pi in_(0)(r^(2)+R^(2)))`

Explanation

`q_(1)+q_(2)=Q`
`sigma4pir^(2)+sigma4piR^(2)=Q`
`sigma=Q/(4pi(r^(2)+R^(2)))`
`V_("centre")=1/(4pi in_(0))[(sigma4pir^(2))/r+(sigmapi R^(2))/R]`
`=(Q(r+R))/(4pi in_(0)(r^(2)+R^(2)))`