1.

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 sigmaof the sheet is proportional to

Answer»

`cos theta`
`tan theta`
`sin theta`
`cot theta`

SOLUTION :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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