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A charged ball B hangs from a silk threa...

A charged ball B hangs from a silk thread S. Which makes an angle 0 with a large charge conducting sheet P as shown in the figure. The surface charge density `sigma` of the sheet is proportional to

A

`cos theta`

B

`tan theta`

C

`sin theta`

D

`cot theta`

Text Solution

Verified by Experts

The correct Answer is:
B
There are three forces exertes on charge in displacement position.
1) Weight mg (downward direction).
(2) Electric force F = Eq (in horizontal direction)
(3) Tension Force T (0 towards P)
Taking two correspondence of tension force
(i) `Tcostheta` = (in upward direction)
(ii) `Tsintheta` = (towards mean position) For balance from figure,
`Tsintheta = qE` and `Tcostheta = mg`
taking ratio `(qE)/(mg) = q/(mg)(sigma/(2epsilon_(0))) [therefore E = sigma/(2epsilon_(0))]`
`therefore tantheta prop sigma` (rest term const) `therefore sigma prop tantheta`
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