Two magnets \( A \) and \( B \) are identical and these are arranged as shown in the figure. The...

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
(A) \( (2 \tan \theta)^{1 / 3} \)
(B) \( (2 \cot \theta)^{1 / 3} \)
(C) \( (2 \tan \theta)^{-1 / 3} \)
(D) \( (2 \cot \theta)^{-1 / 3} \)