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Q.

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

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a

$\tan θ$

b

$\cos θ$

c

$\cot θ$

d

$\sin θ$

answer is B.

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Detailed Solution

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$Tsin θ = qE and Tcos θ = mg$
$\Rightarrow \tan θ = \frac{qE}{mg} = \frac{q}{mg} (\frac{σ}{2 ε_{0}}) \Rightarrow σ \propto \tan θ$

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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