Q.
Two short bar magnets of equal dipole moment $M$ are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance $d$ from the center on the bisector of the right angle is
A) $\frac{\mu_{0}}{4\pi}\frac{2\sqrt{2}M}{d^{3}}$
B) $\frac{\mu_{0}}{4\pi}\ \frac{2M}{d^{3}}$
C) $\frac{\mu_{0}}{4\pi}\frac{M}{d^{3}}$
D) $\frac{\mu_{0}}{4\pi}\frac{2\sqrt{2}M}{d^{3}}$
Explanation
(a) Resolving the magnetic moments along $OP$ and perpendicular to $OP,$ figure we find that component $OP$ perpendicular $OP$ cancel out. Resultant magnetic moment along $OP\ is = M\cos{45{^\circ} + M\ \cos 45{^\circ}}$
[image:5_image46.emf]
$= 2\ M\cos\ 45{^\circ} = \frac{2M}{\sqrt{2}} = \sqrt{2}\ M$
The point $P$ lies on axial line of magnet of moment
$= \sqrt{2}\ M$
$\ \therefore B = \frac{\mu_{0}}{4\pi}\frac{2(\sqrt{2}\ M)}{d^{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.