Q.
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) $\sin\theta$
B) $\tan\theta$
C) $\cos\theta$
D) $\cot\theta$
Explanation
(b) $T\sin\theta = qE$
And $T\cos\theta = mg$
$\Rightarrow \tan\theta = \frac{qE}{mg} = \frac{q}{mg}\left( \frac{\sigma}{2\varepsilon_{0}} \right)$
$\Rightarrow \sigma \propto \tan\theta$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.