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Three concentric metallic spherical shel...

Three concentric metallic spherical shells of radii R, 2R, 3R are given charges `Q_(1) Q_(2) Q_(3)`, respectively. It is found that the surface charge densities on the outer surface of the shells are equal. Then, the ratio of the charges given to the shells `Q_(1) : Q_(2) : Q_(3)` is

A

`1:2:3`

B

`1:3:5`

C

`1:4:9`

D

`1:8:18`

Text Solution

Verified by Experts

The correct Answer is:
B
`sigma=(Q_(1))/(4piR^(2))=(Q_(1)+Q_(2))/(4pi(2R)^(2))=(Q_(1)+Q_(2)+Q_(3))/(4pi(3R)^(2))`
`implies Q_(1)=(Q_(1)+Q_(2))/(4)=(Q_(1)+Q_(2)+Q_(3))/(9)`
`Q_(2)=3Q_(1) and Q_(3)=5Q_(1)`
`Q_(1):Q_(2):Q_(3)=1:3:5`.
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