• # question_answer Two magnets A and B are identical and these are arranged as shown. Their lengths are negligible in comparison to separation between them. A magnetic needle is placed between the magnets at point P and it gets deflected through an angle $\theta .$ The ratio of distances  and will be A) ${{(2\cot \theta )}^{1/3}}$ B) ${{(2\tan \theta )}^{1/3}}$ C) $(2\cot \theta )$             D) ${{(2\tan \theta )}^{-1/3}}$

 Needle will deflect to magnetic field direction at P At P, B is produced by magnet A and B B due to magnet $B={{B}_{1}}$ B due to magnet $A={{B}_{2}}$ Formula of B: At axis of magnet $A=\frac{{{\mu }_{0}}M}{{{d}^{3}}}$ At equatorial axis of magnet $B=\frac{2{{\mu }_{0}}M}{{{d}^{3}}}$ $\therefore {{B}_{2}}=\frac{{{\mu }_{0}}M}{d_{2}^{3}}$ ${{B}_{1}}=\frac{2{{\mu }_{0}}M}{d_{1}^{3}}$
 $\tan \,\,(90=\theta )=\frac{{{B}_{2}}}{{{B}_{1}}}$ $\frac{{{B}_{2}}}{{{B}_{1}}}=\cot \theta$ $\frac{1}{2}{{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{3}}=\cot \theta$ $\frac{d}{{{d}_{2}}}={{(2\cot \theta )}^{1/3}}$