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 tanθ≈sinθ, 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=Tsinθ ....... (i) mg=Tcosθ ........ (ii) tanθ=Femg=q24πϵ0x2×mg also tanθ≈sinθ=x2L Hence x32L=q24πϵ0mg⇒x=(q2L2πϵ0mg)1/3