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5.Magnetism and Matter
hard
Two identical short bar magnets, each having magnetic moment $M,$ are placed a distance of $2d $ apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is
A
$\frac{{{\mu _0}}}{{4\pi }}(\sqrt 2 )\frac{M}{{{d^3}}}$
B
$\frac{{{\mu _0}}}{{4\pi }}(\sqrt 3 )\frac{M}{{{d^3}}}$
C
$\left( {\frac{{2{\mu _0}}}{\pi }} \right)\,\frac{M}{{{d^3}}}$
D
$\frac{{{\mu _0}}}{{4\pi }}(\sqrt 5 )\frac{M}{{{d^3}}}$
(IIT-2000)
Solution
(d)At point $P$ net magnetic field ${B_{net}} = \sqrt {B_1^2 + B_2^2} $
where ${B_1} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2M}}{{{d^3}}}$and ${B_2} = \frac{{{\mu _0}}}{{4\pi }}.\frac{M}{{{d^3}}}$
$ \Rightarrow {B_{net}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{\sqrt 5 M}}{{{d^3}}}$
Standard 12
Physics
