Two identical short bar magnets,each having m | vedclass

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(D) Let the two magnets be placed such that point $P$ is at a distance $d$ from the center of each magnet.For the first magnet,point $P$ lies on its a

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$\frac{\mu_0}{4\pi}(\sqrt{5})\frac{M}{d^3}$

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(D) Let the two magnets be placed such that point $P$ is at a distance $d$ from the center of each magnet.For the first magnet,point $P$ lies on its axial line. The magnetic field due to this magnet at $P$ is $B_1 = \frac{\mu_0}{4\pi} \cdot \frac{2M}{d^3}$.For the second magnet,point $P$ lies on its equatorial line. The magnetic field due to this magnet at $P$ is $B_2 = \frac{\mu_0}{4\pi} \cdot \frac{M}{d^3}$.Since the axes are perpendicular,the fields $B_1$ and $B_2$ are perpendicular to each other.The net magnetic field at $P$ is $B_{net} = \sqrt{B_1^2 + B_2^2}$.Substituting the values: $B_{net} = \sqrt{\left(\frac{\mu_0}{4\pi} \cdot \frac{2M}{d^3}\right)^2 + \left(\frac{\mu_0}{4\pi} \cdot \frac{M}{d^3}\right)^2}$.$B_{net} = \frac{\mu_0}{4\pi} \cdot \frac{M}{d^3} \sqrt{2^2 + 1^2} = \frac{\mu_0}{4\pi} \cdot \frac{\sqrt{5}M}{d^3}$.

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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