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

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

Answer 1

The correct option is B $tan\theta$

Balancing the forces in the horizontal direction we get,
$Tsin\theta =qE$..............(i)
and in the vertical direction we get,

$Tcos\theta =mg$.............(ii)

Dividing (i) by (ii) we get,
$\Rightarrow tan\theta =\frac{qE}{mg}=\frac{q}{mg}\left(\frac{\sigma }{2\pi {ϵ}_0}\right)$

Since electric field due to a large charged conducting sheet is $\frac{\sigma }{2\pi {ϵ}_0}$.
$\Rightarrow \sigma \propto tan\theta$.