Two identical bar magnets of magnetic moment M each, are placed along X and Y- axes, respectively at a distance d from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on X – axis and on the magnetic axis of magnet placed on Y – asix. If the magnigtude of total magnetic field at the orgin is $B = α [\frac{μ_{0}}{4 π} \frac{M}{d^{3}}]$ then the value of constant will be (d > > l, where l is the length of the bas magnets and direction of N to S in magnets is opposite with respect to each other)

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$\sqrt{5}$

answer is C.

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Detailed Solution

Magnetic field due to axial magnet,
$B_{1} = \frac{μ_{o}}{4 π} \frac{2 M}{d^{3}}$ (+ Y direction)
Magnetic field due to the equatorial magnet,
$B_{2} = \frac{μ_{o}}{4 π} \frac{2 M}{d^{3}}$ (+ Y direction)
So, effective magnetic field
$B = B_{1} + B_{2} = 3 \frac{μ_{o} M}{4 π d} \Rightarrow α = 3$