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_1/R_2`
B. `R_2/R_1`
C. `sqrt((R_1/R_2))`
D. `R_1^2/R_2^2`

Answer

B

Explanation

When connected by wire, potential is equal
`V_1=V_2 implies (KQ_1)/(R_1)=(KQ_2)/(R_2)`
`implies Q_1/Q_2=R_1/R_2`
Surface charge density `(sigma) = ("charge")/("area")`
`implies (sigma_1)/(sigma_2)=Q_1/Q_2xx(4piR_2^2)/(4piR_1^2)=R_1/R_2xxR_2^2/R_1^2`
`implies (sigma_1)/(sigma_2)=R_2/R_1`