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)/(2)sqrt(3)`
B. `(Q)/(4)sqrt(2)`
C. `(Q)/(3)sqrt(2)`
D. `(Q)/(4)sqrt(3)`

Answer

B

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)/(2sqrt(2)R^(2))` directed towards the centre.

Electric field at `P` due to centre charge: `(kq)/(R^(2))` for net field to be zero at `P`:
`(kq)/(R^(2))=(kQ)/(2sqrt(2)R^(2))implies q=(Q)/(2sqrt(2))=(Q)/(4)sqrt(2)`