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 a point on the axis of the ring at distant R from the center of the ring.

Options

A. Q
B. `(Q)/(2)`
C. `(Q)/(2sqrt(2))`
D. `2sqrt(2)Q`

Answer

C

Explanation

Electric field at point P due to charge of ring is `E=(k Q x)/((R^2+x^2)^(3//2))`
At x= R, `E_(ring)=(KQ)/(2sqrt2 R^2)`
Electric field at P due to center charge is `Kq//R^2` directed away form the center. For net field to be zero at P
`(Kq)/R^2=(kQ)/(2sqrt2 R^2) or q=Q/(2sqrt2)`