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Question

# A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to

A
sin θ
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B
tan θ
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C
cos θ
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D
cot θ
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Solution

## The correct option is B tan θBalancing the forces in the horizontal direction we get, T sin θ=qE..............(i) and in the vertical direction we get,T cos θ=mg.............(ii)Dividing (i) by (ii) we get, ⇒tan θ=qEmg=qmg(σ2πϵ0)Since electric field due to a large charged conducting sheet is σ2πϵ0. ⇒σ∝ tan θ.

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