Two insulated charged conducting spheres of radii `20 cm` and `15 cm` respectively and having an equal charge of `10 C` are connected by a copper wire and then they are separted. Then

Options

A. both the spheres will have the same charge of `10 cm`
B. surface charge density on the `20 cm` sphere will be greater than that on the `15 cm` sphere
C. surface charge density on the `15 cm` sphere will be greater than that on the `20 cm` sphere
D. surface charge density on the two spheres will be equal

Answer

C

Explanation

After redistribution, charges on them will be different, but they will acquire common potential i.e.,
`k(Q_(1))/(r_(1)) = k(Q_(2))/(r_(2)) rArr (Q_(1))/(Q_(2)) = (r_(1))/(r_(2))`
As `sigma = (Q)/(4pi r^(2)) rArr = (sigma_(1))/(sigma_(2)) = (Q_(1))/(Q_(2)) xx (r_(2)^(2))/(r_(1)^(2))`
`rArr (sigma_(1))/(sigma_(2)) = (r_(2))/(r_(1)) rArr prop (1)/(r )`
i.e., surface charge density on smaller sphere will be more.