Consider two uniformaly charged concentric and coaxial rings of radii R and 2R. Total charge on inner ring is `Q_(1)` and that on outer ring is `Q_(2)`. Both rings are revolving in same sence with same angular velocity about its axis. If net magnetic induction at a distance R feom the centre of the rings, on axis of rings is zero then `(Q_(1))/(Q_(2))` is :

Options

A. `-1`
B. `-(2sqrt(2))/(5sqrt(5))`
C. `-(8sqrt(2))/(5sqrt(5))`
D. `-(4sqrt(2))/(3sqrt(3))`

Explanation

Magnetic field due to circular current carrying loop on axis of loop is:
`B=(mu_(0))/(4pi)(2IpiR^(2))/((R^(2)+X^(2))^(3//2))=0`
`B_(1)+B_(2)=0`
`(Q_(1)R_(2))/((R^(2)+R^(2))^(3//2))+(Q_(2)4R^(2))/((4R^(2)+R^(2))^(3//2))=0`
`(Q_(1))/(2sqrt(2))+(Q_(2)4)/(5sqrt(5))=0`
`(Q_(1))/(Q_(2))=(8sqrt(2))/(5sqrt(5))`