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In a ring having linear charge density l...

In a ring having linear charge density `lambda`, made up of wire of cross-section area `A`, young modulus `y, a` charge `Q_(0)` is placed at it's centre. If initial radius is `'R'`, then find out change in radius

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Considering an element of angular width `2theta`-
`dq = gammaR'. 2theta rArr F = 2T sin theta`
`(kdq.Q_(0))/(R'^(2)) = 2Tsintheta rArr (kgammaR' xx 2theta.Q_(0))/(R'^(2)) = 2T sintheta`
If `theta` is small, then `sin theta = 0`
further `(klambdaQ_(0))/(R') = T`
But `Y = ("stress")/("strain"), "strain" = (2pi(R' - R))/(2piR) = (R' - R)/(R)`
`Y = (T)/(a(R' - R)) rArr R' - R = (klambdaQ_(0))/(R'AY)`
`Y = (T)/(A(DeltaR)/(R)) rArr DeltaR = (TR)/(AY) = (klambdaQ_(0)R)/(R'AY) = (klambdaQ_(0))/(AY), (R = R')`
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