Q. A compass needle placed at a distance $r$ from a short magnet in a tan $A$ position shows a deflection of 60${^\circ}$. If the distance is increased to $r(2)^{1/3}$, the deflection of compass needle is
A) 30${^\circ}$
B) 60${^\circ}$
C) 45${^\circ}$
D) 0${^\circ}$
Explanation
(a) $\frac{\tan\theta_{2}}{\tan\theta_{1}} = \frac{d_{1}^{3}}{d_{2}^{3}} = \frac{r^{3}}{\left\lbrack r(3)^{1/3} \right\rbrack^{3}} = \frac{1}{3}$
$\tan\theta_{2} = \frac{1}{3}\ tan\theta_{1} = \frac{tan60{^\circ}}{3} = \frac{\sqrt{3}}{3} = \frac{1}{\sqrt{3}}$
$\therefore\theta_{2} = 30{^\circ}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.