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Two short magnets of equal dipole moments $M $ are fastened perpendicularly at their centre (figure). The magnitude of the magnetic field at a distance $d $ from the centre on the bisector of the right angle is
$\frac{{{\mu _0}}}{{4\pi }}\frac{M}{{{d^3}}}$
$\frac{{{\mu _0}}}{{4\pi }}\frac{{M\sqrt 2 }}{{{d^3}}}$
$\frac{{{\mu _0}}}{{4\pi }}\frac{{2\sqrt 2 M}}{{{d^3}}}$
$\frac{{{\mu _0}}}{{4\pi }}\frac{{2M}}{{{d^3}}}$
Solution
(c)Resultant magnetic moment of the two magnets is
${M_{net}} = \sqrt {{M^2} + {M^2}} = \sqrt 2 M$
Imagine a short magnet lying along $OP$ with magnetic moment equal to $M\sqrt 2 $. Thus point $P$ lies on the axial line of the magnet.
$\therefore $ Magnitude of magnetic field at $P$ is given by $B = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\sqrt 2 M}}{{{d^3}}}$
