Two identical bar magnets each of magnetic moment 'M', separated by some distance are kept perpendicular to…

Two identical bar magnets each of magnetic moment 'M', separated by some distance are kept perpendicular to each other. The magnetic induction at a point at the same distance 'd' from the centre of magnets, is $\quad\left(\mu_{0}=\right.$ permeability of free space $)$
  1. $\frac{\mu_{0}}{4 \pi}(\sqrt{2}) \frac{\mathrm{M}}{\mathrm{d}^{3}}$
  2. $\frac{\mu_{0}}{4 \pi}(\sqrt{3}) \frac{M}{d^{3}}$
  3. $\left(\frac{2 \mu_{0}}{\pi}\right) \frac{\mathrm{M}}{\mathrm{d}^{3}}$
  4. $\frac{\mu_{0}}{4 \pi}(\sqrt{5}) \frac{\mathrm{M}}{\mathrm{d}^{3}}$

Solution

$\mathrm{B}_{1}=\frac{2 \mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}}$ at axial position $\mathrm{B}_{2}=\frac{\mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}}$ at equatorial position $\mathrm{B}_{\mathrm{Net}}=\sqrt{\mathrm{B}_{1}^{2}+\mathrm{B}_{2}^{2}}$ $=\frac{\mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}} \sqrt{5}$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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