Question

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. $(2 \tan \theta)^{-1 / 3}$
• C. $(2 \cot \theta)^{1 / 3}$
• D. $(2 \cot \theta)^{-1 / 3}$

Answer 1

Answer: (C)

In equilibrium, $B_{1}=B_{2} \tan \theta$

$\Rightarrow \frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{d_{1}^{3}}=\frac{\mu_{0}}{4 \pi} \cdot \frac{M}{d_{2}^{3}} \tan \theta$
$\Rightarrow \frac{d_{1}}{d_{2}}=(2 \cot \theta)^{1 / 3}$