A thin circular wire of radius r has a charge Q. If a point charge q is placed at the centre of the ring, then find the increase in tension in the wire.

Answer

`(qQ)/(8pi^(2) in_(0) r^(2))`

Explanation

We consider an element subtending angle `dtheta` at the centre

F=electrostatic force on element
`=(KdQ.q)/R^(2)=(((KQ)/(2piR)xxRd theta))/R^(2)q=(KQq)/(2pi R^(2))d theta`
`2T "sin" (d theta)/2cong2Txxtheta/2=(KQqd theta)/(2pi R^(2)) :. T=(Qq)/(8pi^(2)in_(0)r^(2))`