Two charged spherical conductors of radius `R_1` and `R_2` are connected by a wire. Then the ratio of surface charge densities of the spheres `(sigma_1)/(sigma_2)` is

Options

A. `R_2/R_1`
B. `sqrt(((R_1)/(R_2)))`
C. `R_1^2/R_2^2`
D. `R_1/R_2`

Answer

A

Explanation

The potential will be equal as they are connected with wire.
`k(q_1)/(R_2) = k(q_2)/(R_1)`
`implies q_1/q_2=R_1/R_2implies sigma_1/sigma_2=(q_1//4piR_1^2)/(q_2//4piR_2^2)`
`=(q_1)/(q_2)((R_2)/(R_1))^2`
`:. sigma_1/sigma_2 =R_2/R_1`