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

    $\frac{{{\mu _0}}}{{4\pi }}\,\left( {\sqrt 2 } \right)\frac{M}{{{d^3}}}$

  • B

    $\frac{{{\mu _0}}}{{4\pi }}\,\left( {\sqrt 3 } \right)\frac{M}{{{d^3}}}$

  • C

    $\left( {\frac{{2{\mu _0}}}{\pi }} \right)\,\frac{M}{{{d^3}}}$

  • D

    $\frac{{{\mu _0}}}{{4\pi }}\,\left( {\sqrt 5 } \right)\frac{M}{{{d^3}}}$

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  • [AIEEE 2005]