A conducting sphere of radius `10 cm` is charged `10 muC`. Another uncharged sphere of radius `20 cm` is allowed to touch it for some tome. After that if the sphere are separted, then surface density of chsrges, on the spheres will be in the ratio of

Options

A. `1 : 1`
B. `4 : 1`
C. `1 : 3`
D. `1 : 4

Answer

B

Explanation

(b) When one charged and other uncharged conducting spheres are in contact then charge on each sphere is half the charge on first charged sphere.
When both the spheres are placed in contact with each other, the charge on each,
`q_(1) = q_(2) = q = (10 + 0)/(2) muC = 5 mu C`
Surface charge density is given by, `sigma = (q)/(4 pi r)`
Hence, `sigma_(1) = (q_(1))/(4 pi r_(1)^(2))` and `sigma_(2) = (q_(2))/(4 pi r_(2)^(2))`
`implies (sigma_(1))/(sigma_(2)) = (q_(1))/(4 pi r_(1)^(2)) (4 pi_(2)^(2))/(q_(2)) = (5 xx (20)^(2))/((10)^(2) xx 5) = (4)/(1)`