A charged ball B hangs from a silk thread S, which makes an angle… - Vidyadip

MCQ

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

A
$\sin \theta $
✓
$\tan \theta $
C
$\cos \theta $
D
$\cot \theta $

✓

Answer

Correct option: B.

$\tan \theta $

b
(b) $T\sin \theta = qE$
and $T\cos \theta = mg$
$==>$ $\tan \theta = \frac{{qE}}{{mg}} = \frac{q}{{mg}}\,\left( {\frac{\sigma }{{2{\varepsilon _0}}}} \right)$
$==>$ $\sigma \propto \tan \theta $.

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