Question

A short bar magnet placed at a certain distance from D.M.M in tan A position produces a deflection of ${60}^o$. The magnet is now cut into $3$ equal pieces. If one piece is kept at same distance in $\tan A$ from D.M.M, then the deflection produced is

• A. ${10}^o$
• B. ${20}^o$
• C. ${30}^o$
• D. ${60}^o$

Answer 1

Answer: (C)

${30}^o$

$M_1=PoleStrength\times l$
When the magnet is cut into 3 pieces, both mass and length become $\frac{1}{3}$ rd of the previous ones, but pole strength does not change.
$M_2=PoleStrength\times \frac{l}{3}=\frac{M_1}{3}$
Given, ${\theta }_1={60}^{\circ }$
$\therefore \tan {\theta }_2=\frac{M_2}{M_1}\tan {\theta }_1=\frac{1}{3}\times \tan {60}^{\circ }=\frac{1}{3}\times \sqrt{3}=\frac{1}{\sqrt{3}}$
$\Rightarrow {\theta }_2={30}^{\circ }$