Two metal spheres A and B of radius r and 2r whose centres are separated by a distance of 6r are given charge Q, are at potential ` V_1 and V_2 `. Find theratio of ` V_1//V_2 ` . These spheres are connected to each other with the help of a connecting wire keeping the separation unchanged, what is the amount of charge that will flow through the wire ?

Explanation

`V_1 = (kq)/(r ) + (kq)/(6r) = (7 kq )/(6r ) `
` V_2 = (kq)/(2r) + (kq)/(6r) = (3kq + kq )/(6r) = (4kq )/(6r) `
` (V_1)/(V_2) = (7)/(4) `
`V_("common") = (2q )/( 4pi epsi _0(r + 2r))= (2q)/(12 pi epsi _0 r ) = V. `
Charge transferred equal to
` q.= C_1 V_1 - C_1 V. = (r )/(k) (kq)/(r ) - (r)/(k) (k_2 q )/(3r) `
` = q - (2q)/(3) = (q )/(3 )`.