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 tan theta)^(1//3)`
B. `(2 tan theta)^(-1//3)`
C. `(2 cot theta)^(1//3)`
D. `(2 cot theta)^(-1//3)`

Answer

C

Explanation

`implies (mu_0)/(4pi) cdot (2M)/(d_(1)^(3)) = (mu_0)/(4pi).(M)/(d_(2)^(3)) tan theta`
`implies (d_1)/(d_2) = (2cot theta)^(1/3)`.