Two identical bar magnets,each of magnetic mo | vedclass

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Question

(D) For a bar magnet of magnetic moment $M$,the magnetic field at an axial point at distance $d$ is $B_{axial} = \frac{\mu_{0}}{4 \pi} \frac{2M}{d^{3}

Vedclass · Accepted Answer

$\frac{\mu_{0}}{4 \pi}(\sqrt{5}) \frac{M}{d^{3}}$

Vedclass · Answer

(D) For a bar magnet of magnetic moment $M$,the magnetic field at an axial point at distance $d$ is $B_{axial} = \frac{\mu_{0}}{4 \pi} \frac{2M}{d^{3}}$.For the same magnet,the magnetic field at an equatorial point at distance $d$ is $B_{equatorial} = \frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}}$.Since the magnets are perpendicular,the point at distance $d$ from both centers acts as an axial point for one magnet and an equatorial point for the other.The resultant magnetic field is $B_{net} = \sqrt{B_{axial}^{2} + B_{equatorial}^{2}}$.Substituting the values: $B_{net} = \sqrt{\left(\frac{\mu_{0}}{4 \pi} \frac{2M}{d^{3}}\right)^{2} + \left(\frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}}\right)^{2}}$.$B_{net} = \frac{\mu_{0} M}{4 \pi d^{3}} \sqrt{2^{2} + 1^{2}} = \frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}} \sqrt{5}$.

Two identical bar magnets,each of magnetic moment $M$,are kept perpendicular to each other at a certain distance. The magnetic induction at a point that is at the same distance $d$ from the center of both magnets is: (where $\mu_{0}$ is the permeability of free space)

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