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Question

# Three concentric conducting spherical shells have radii r,2r and 3r and charges q1,q2 and q3 respectively. Innermost and outermost shells are earthed as shown in the figure, then ratio of magnitudes of q1,q2 and q3 is

A
3:4:3
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B
1:3:3
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C
4:4:3
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D
1:4:3
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Solution

## The correct option is D 1:4:3 Potential of innermost shell is zero. ∴q1r+q22r+q33r=0 6q1+3q2+2q3=0 ... (1) Similarly, potential on outermost shell is also zero. ∴q13r+q23r+q33r=0 q1+q3=−q2 ... (2) Solving equations (1) and (2), we get q1=−q24,q3q1=3 and q3q2=−34 Hence q1:q2:q3=1:−4:3 Ratio of magnitudes of charges is 1:4:3

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