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A simple penduclum of length l and bob m...

A simple penduclum of length `l` and bob mass `m` is hangind in front of a large nonconducting a having surface charge density `sigma`. If suddenly a charge `+q` is given to the bob `&` it is released from the position shown in figure. Find the maximum angle through which the string is deflected from vertical .
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Text Solution

Verified by Experts

The correct Answer is:
` 2 tan^(-1) ((sigma_0)/(2 varepsilon_0 mg))`.
From conservation of energy Gain in gravitation `P.E`. = work work done by electric field
`mg l (1 - cos theta ) = q E sin theta`
`mg xx 2 sin^2 (theta)/2 qE sin (theta)/2 cos (theta)/2`
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`mg sin (theta)/2 = q E cos (theta)/2`
`tan (theta)/2 = (qE)/(mg) ( put E = (sigma)/(2 in_0))`
`tan (theta)/2 = (qE)/(2 in_0 mg) rArr theta =2 tan^(-1) (q singa)/( 2 in_0 mg)`.
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