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 $B_1=B_2 \tan \theta$
$\Rightarrow \frac{\mu_0}{4 \pi} \cdot \frac{2 M}{d_1^3}=\frac{\mu_0}{4 \pi} \cdot \frac{M}{d_2^3} \tan \theta$
$\Rightarrow \frac{d_1}{d_2}=(2 \cot \theta)^{1 / 3}$