A point charge Q is located at centre of a fixed thin ring of radius R with uniformly distribute charge -Q. The magnitude of the electric field strength at the point lying on the axis of the ring at a distance x from the centre is `(x gt gt R)`

Explanation

Electric field at P due ring
`E_(1)=(qx)/(4pi in_(0) (x^(2)+R^(2))^(3//2))` (towards centre)
Electric field at P due to +q
`E_(2)=(q)/(4pi in_(0)x^(2))` (away from centre)
Thus net field at P is `E_("Net") =E_(1)+E_(2)`
`=(q)/(4pi in_(0)) [(1)/(x^(2)) -(x)/((x^(2)+R^(2))^(3//2))]`
For `x gt gt R`
`E_("net")=(q[(x^(2)+R^(2))^(3//2)-x^(3)])/(4pi in_(0)x^(2)(x^(2)+R^(2))^(3//2))`
`=(3qR^(2))/(4pi in_(0) 2x^(4))=(3qR^(2))/(8pi in_(0)x^(4))`
(Using Binomial approximation).