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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
$\frac{{{\mu _0}}}{{4\pi }}\,\left( {\sqrt 2 } \right)\frac{M}{{{d^3}}}$
$\frac{{{\mu _0}}}{{4\pi }}\,\left( {\sqrt 3 } \right)\frac{M}{{{d^3}}}$
$\left( {\frac{{2{\mu _0}}}{\pi }} \right)\,\frac{M}{{{d^3}}}$
$\frac{{{\mu _0}}}{{4\pi }}\,\left( {\sqrt 5 } \right)\frac{M}{{{d^3}}}$
Solution
At point $P$ net magnetic field ${B_{n\infty }} = \sqrt {B_1^2 + B_2^2} $
where ${{\text{B}}_1} = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{2{\text{M}}}}{{{{\text{d}}^3}}}\,and\,{{\text{B}}_2} = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{\text{M}}}{{{{\text{d}}^3}}}$
$ \Rightarrow {{\text{B}}_{{\text{rest}}}} = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{\sqrt 5 {\text{M}}}}{{{{\text{d}}^3}}}$
