Question

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 given figure. The surface charge density $\sigma$ of the sheet is proportional to :

• A. $cos\theta$
• B. $cot\theta$
• C. $sin\theta$
• D. $tan\theta$

Answer 1

The correct option is D $tan\theta$

Resolve $T:

$Tcos\theta =mg$ .....(1)
$Tsin\theta =qE=q\frac{\sigma }{{\epsilon }_0}$ ......(2)
Divide Eq (2) by (1)
$tan\theta =\frac{q\sigma }{mg{\epsilon }_0}i$
$\Rightarrow \sigma \propto tan\theta$
Hence, the correct answer is $\left(D\right)$