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A ring of radius R has charge -Q distrib...

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.

A

Q

B

`(Q)/(2)`

C

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

D

`2sqrt(2)Q`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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