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A simple pendulum of length l abd bob ma...

A simple pendulum of length l abd bob mass m is hanging in front of a large nonconducting sheet having surface charge density `sigma`. If suddenly a charge +q is given to the bob and it released from the position shown in (Fig. 3.87), 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) ((sigmaq_(0))/(2in_(0) mg))`
From work energy theorem (WET)

`W_(EF)+W_(mg)=Delta KE`
`q_(0) xx sigma/(2 in_(0))xxL sin theta-mgL`
`(1- cos theta)=0`
`=q_(0)xx sigma/(2 in_(0))xxLxx2 "sin" theta/2 "cos" theta/2`
`=mgLxx2 "sin"^(2) (2 theta)/2, "tan" theta/2=sigma/(2 in_(0))xxq_(0)/(mg)`
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