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Three concentric conducting spherical sh...

Three concentric conducting spherical shells have radii r, 2r, and 3r and charges `q_1,q_2 and q_3`, respectively. Innermost and outermost shells are earthed as shown in figure. The charges shown are after earthing. Select the correct alternative.

A

`Q_(1)+Q_(3)=-Q_(2)`

B

`Q_(1)=(-Q_(2))/4`

C

`Q_(3)/Q_(1)=3`

D

`Q_(3)/Q_(2)=(-1)/3`

Text Solution

Verified by Experts

The correct Answer is:
D

Potential at outermost shell
`=(KQ_(1))/(3r)+(KQ_(2))/(3r)+(KQ_(3))/(3r)=0`
`rArr Q_(1)+Q_(2)+Q_(3)=0` …(i)
and potential at innermost surface
`(KQ_(1))/(r)+(KQ_(2))/(2r)+(KQ_(3))/(3r)=0`
`rArr (K[6Q_(1)+3Q_(2)+2Q_(3)])/(6r)=0` ...(ii)
From eq. (i) & (ii) `Q_(1)=-Q_(2)/4` and also `Q_(2)/Q_(1)=3`
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