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A circular ring of radius R with uniform...

A circular ring of radius R with uniform positive charge density `lambda` per unit length is located in the y-z plane with its centre at the origin O. A particle of mass m and positive charge q is projected from the point P `(Rsqrt3, 0, 0)` on the positive x-axis directly towards O, with an initial speed v. Find the smallest (non-zero) value of the speed v such that the particle does not return to P.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt((lambda q)/(2 in_(0)m))`

K.E. at 'P' must be sufficient to reach the charge particle at the centre of the ring.
`(ME)_(P)=(ME)_("centre of ring")`
`1/2 mv^(2)+(Kpi lambdaxx2pi Rq)/sqrt((R^(2)+sqrt(3)R)^(2))=O+(Kxxlambda2piRq)/(R)`
`v=sqrt((lambdaq)/(2in_(0)m)) ( :' K=1/(4pi in_(0)))`
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