MHT CET · Physics · Magnetic Effects of Current
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 \()\)
- A \(\frac{\mu_{0}}{4 \pi}(\sqrt{2}) \frac{\mathrm{M}}{\mathrm{d}^{3}}\)
- B \(\frac{\mu_{0}}{4 \pi}(\sqrt{3}) \frac{M}{d^{3}}\)
- C \(\left(\frac{2 \mu_{0}}{\pi}\right) \frac{\mathrm{M}}{\mathrm{d}^{3}}\)
- D \(\frac{\mu_{0}}{4 \pi}(\sqrt{5}) \frac{\mathrm{M}}{\mathrm{d}^{3}}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mu_{0}}{4 \pi}(\sqrt{5}) \frac{\mathrm{M}}{\mathrm{d}^{3}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{B}_{1}=\frac{2 \mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}}\) at axial position
\(\mathrm{B}_{2}=\frac{\mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}}\) at equatorial position
\(\mathrm{B}_{\mathrm{Net}}=\sqrt{\mathrm{B}_{1}^{2}+\mathrm{B}_{2}^{2}}\)
\(=\frac{\mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}} \sqrt{5}\)
\(\mathrm{B}_{2}=\frac{\mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}}\) at equatorial position
\(\mathrm{B}_{\mathrm{Net}}=\sqrt{\mathrm{B}_{1}^{2}+\mathrm{B}_{2}^{2}}\)
\(=\frac{\mathrm{M} \mu_{0}}{4 \pi \mathrm{d}^{3}} \sqrt{5}\)
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