Q. 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) $\left( 2\tan\theta \right)^{1/3}$
B) $\left( 2\tan\theta \right)^{- 1/3}$
C) $\left( 2\cot\theta \right)^{1/3}$
D) $\left( 2\cot\theta \right)^{- 1/3}$
Explanation
(c) In equilibrium $B_{1} = B_{2}\tan\theta$
$\Rightarrow \frac{\mu_{0}}{4\pi}.\frac{2M}{d_{1}^{3}} = \frac{\mu_{0}}{4\pi}.\frac{M}{d_{2}^{3}}\tan\theta$
$\Rightarrow \frac{d_{1}}{d_{2}} = \left( 2\cot\theta \right)^{1/3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.