Question

Two short bar magnets $\text{A}$ and $\text{B}$ are identical and these are arranged as shown in the figure. A magnetic needle is placed between the magnets at point $\text{P}$ which gets deflected through an angle $\theta$ under the influence of magnets. The ratio of distances ${\text{d}}_1$ and ${\text{d}}_2$ will be.

• A. $\frac{1}{\sqrt[3]{32\tan \theta }}$
• B. $\frac{1}{\sqrt[3]{32\cot \theta }}$
• C. $\sqrt[3]{32\cot \theta }$
• D. $\sqrt[3]{32\tan \theta }$

Answer 1

The correct option is C $\sqrt[3]{32\cot \theta }$

Due to both the fields,


$\tan \theta =\frac{{\text{B}}_{a{x}_1}}{{\text{B}}_{e{q}_2}}$

$\Rightarrow \tan \theta =\left(\frac{\frac{{\mu }_{0}2M}{4\pi {d_1}^3}}{\frac{{\mu }_{0}M}{4\pi {d_2}^3}}\right)$

$\Rightarrow \tan \theta =2{\left(\frac{d_2}{d_1}\right)}^3$

$\Rightarrow \frac{d_1}{d_2}={\left(2\cot \theta \right)}^{1/3}$