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

Answer 1

The correct option is C $(2cot\theta {)}^{\frac{1}{3}}$


In equilibrium $B_1=B_{2}tan\theta$


$\Rightarrow$ $\frac{{\mu }_0}{4\pi }.\frac{2M}{d_1^3}=\frac{{\mu }_0}{4\pi }.\frac{M}{d_2^3}tan\theta$
$\Rightarrow$ $\frac{d_1}{d_2}=(2cot\theta {)}^{\frac{1}{3}}$