Two magnets `A` and `B` are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle `theta` under the influence of magnets. The ratio of distance `d_(1)` and `d_(2)` will be

Options

A. `(2 tantheta)^(1//3)`
B. `(2 tantheta)^(-1//3)`
C. `(2 cottheta)^(1//3)`
D. `(2 cottheta)^(-1//3)`

Answer

C

Explanation

In euilibrium `B_(1)=B_(2) tantheta`

`impliesmu_(0)/(4pi).(2M)/d_(1)^(3)=mu_(0)/(4pi).M/b_(2)^(3) tan theta`
`implies d_(1)/d_(2)=(2 cottheta)^(1//3)`