A ring of radius R has charge `-Q` distributed uniformly over it. Calculate the charge that should be placed at the center of the ring such that the electric field becomes zero at apoint on the axis of the ring at distant R from the center of the ring.

Answer

`(Q)/(2 sqrt(2))`

Explanation

Electric field at point P due to charge of ring is
`E=(kQx)/((R^(2)+x^(2))^(3//2))`
At `x=R, E=(kQ)/(2 sqrt(2)R^(2))` directed toward the center
Electric fild at P due to charge at center , `kq//R^(2)`.
For net field to be zero at P
`(kq)/(R^(2))=(kQ)/(2 sqrt(2)R^(2))` or `q=(Q)/(2 sqrt(2))`.