A ring of radius `R` is with a uniformly distributed charge `Q` on it .A charge `q` is now placed in the centre of the ring .Find the increment in tension in the ring.

Explanation

Consider an elecment of the ring. The enlarged view is as shown. For equilibrium of this segment, we can write.


`F=2 DeltaT sin ((d theta)/2)`
Here F is he repulsive force between q and element charge dQ
`[ :. dQ =Q/(2pi R) (R d theta)]`
The electric outward force on elemen is
`F=1/(4 pi epsilon_(0)) (qdQ)/(R^(2))`
From the above three equations, we can write
`1/(4 pi epsilon_(0)) q/(R^(2))(QRd theta)/(2 pi R)=2 DeltaT((d theta)/2)`
`( :. sin alpha = alpha` for small angle )