Question

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
\textit{( \( \mu_0 \) = permeability of free space)}

• A. \( \frac{\mu_0}{4\pi} \left( \sqrt{2} \right) \frac{M}{d^3} \)
• B. \( \frac{\mu_0}{4\pi} \left( \sqrt{3} \right) \frac{M}{d^3} \)
• C. \( \frac{2\mu_0}{\pi} \frac{M}{d^3} \)
• D. \( \frac{\mu_0}{4\pi} \left( \sqrt{5} \right) \frac{M}{d^3} \)

Hint:

When calculating the magnetic induction due to multiple magnetic fields, use vector addition and consider their directions carefully.

Answer 1

The Correct Option is D

Step 1: Magnetic induction of two perpendicular bar magnets.
When two bar magnets are placed perpendicular to each other, the magnetic induction at a point is calculated by the vector sum of the magnetic fields of each magnet. For two identical bar magnets, the resultant magnetic induction at a point at a distance \( d \) is given by: \[ B = \frac{\mu_0}{4\pi} \left( \sqrt{5} \right) \frac{M}{d^3} \]
Step 2: Conclusion.
Thus, the correct answer is (D) \( \frac{\mu_0}{4\pi} \left( \sqrt{5} \right) \frac{M{d^3} \)}.