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Question

In the given figure two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of equal length L. Assume that θ is so small that tan θsin θ, then for equilibrium x is equal to



A
(q2L2πϵ0mg)1/3
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B
(qL22πϵ0mg)1/3
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C
(q2L24πϵ0mg)1/3
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D
(q2L4πϵ0mg)1/3
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Solution

The correct option is A (q2L2πϵ0mg)1/3

In equilibrium Fe=T sin θ ....... (i)
mg=T cos θ ........ (ii)
tan θ=Femg=q24πϵ0x2×mg also tan θsin θ=x2L
Hence x32L=q24πϵ0mgx=(q2L2πϵ0mg)1/3


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