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.

Explanation

Consider an element. Its enlarged view is as shown. For equilibrium of this segment, we can write.
`F= 2DeltaT sin ((d theta)/(2))`
Here F is the repulsive force between q and elemental charge dQ
`dQ=(Q)/( 2pi R) (Rd theta)`
The electric outward force on element is
`F=(1)/(4pi in_(0)) (qdQ)/( R^(2))`
From the above three equations, we can write
`(1)/(4pi in_(0)) (q)/(R^(2)) (QRd theta)/(2piR) ~~ 2DeltaT((d theta)/(2))`
(`:. sin alpha = alpha` for small angle)
`Delta = (Qq)/( 8pi^(2) in_(0) R^(2))`