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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

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$\frac{μ_{0}}{4 π} (\sqrt{2}) \frac{M}{d^{3}}$

$\frac{μ_{0}}{4 π} (\sqrt{3}) \frac{M}{d^{3}}$

$(\frac{2 μ_{0}}{π}) \frac{M}{d^{3}}$

$\frac{μ_{0}}{4 π} (\sqrt{5}) \frac{M}{d^{3}}$

answer is D.

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Detailed Solution

$B = \sqrt{B_{1}^{2} + B_{2}^{2}}$

$B_{1} = B_{axial} = \frac{2 μ_{o} M}{4 {πd}^{3}}$

$B_{2} = B_{equa} = - \frac{μ_{o} M}{4 {πd}^{3}}$

$\Rightarrow B = \sqrt{5} \frac{μ_{0}}{4 π} \frac{M}{d^{3}}$

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