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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 denisties on the outer surfaces 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
`Q_(1)=sigma4pi R^(2)=k` (say)
`Q_(1)+Q_(2)=sigma4pi(4R^(2))=4k`
`Q_(1)+Q_(2)+Q_(3)=sigma(4pi)(9r^(2))=9k`
On solving, `Q_(1):Q_(2):Q_(3) : : 1:3:5`
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