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A charged ball from a silk thread, which...

A charged ball from a silk thread, which makes an angle `theta` with a large charged conducting sheet. The surface charge density `sigma` of the sheet is proportional to…..

A

`tan theta`

B

`sin theta`

C

`cos theta`

D

`cot theta`

Text Solution

Verified by Experts

The correct Answer is:
A

As shown in the figure If T is the tension produced in the string then if `F_e` is electric force then,
(i) For horizontal equilibrium of bob,
`T sin theta- F_q= qE=q(sigma/(2in_0))`…..(1)
(ii) For vertical equilibrium of bob
`T cos theta= mg`.......(2)
Taking ratio of equation (1) to equation (2)
`T cos theta= mg and T sin theta= (q sigma)/(2 in_0)`
`therefore (T sin theta)/(T cos theta)= sigma/(2in_0) times q/(mg)`
`therefore tan theta= (q/(2 in_0 mg)). sigma`
`therefore tan theta infty sigma`[ `because` Remaining terms are constant]
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