Question

The dipole moment of the short bar magnet is \( 12.5 \, \text{A} \cdot \text{m}^2 \). The magnetic field on its axis at a distance of \( 0.5 \, \text{m} \) from the centre of the magnet is

• A. \( 1.0 \times 10^{-4} \, \text{N/A} \cdot \text{m} \)
• B. \( 4 \times 10^{-4} \, \text{N/A} \cdot \text{m} \)
• C. \( 2 \times 10^{-4} \, \text{N/A} \cdot \text{m} \)
• D. \( 6.64 \times 10^{-8} \, \text{N/A} \cdot \text{m} \)

Hint:

For a magnetic dipole, the magnetic field on its axis is inversely proportional to the cube of the distance.

Answer 1

The Correct Option is A

The magnetic field on the axis of a dipole is given by \( B = \frac{\mu_0 m}{2\pi r^3} \), where \( m \) is the magnetic dipole moment and \( r \) is the distance from the dipole. Substituting the given values, we find the magnetic field at the specified distance.

Step 2: Conclusion.
The magnetic field is \( 1.0 \times 10^{-4} \, \text{N/A} \cdot \text{m} \), corresponding to option (a).