Question

The magnetic field due to a short bar magnet at an axial point at a distance \( r \) from its centre is \( B \). If this axis is moved towards the equator of the magnet along a circular path of radius \( r \), then the magnetic field \( B \) will

• A. not change
• B. go on increasing
• C. increase from zero to infinity
• D. go on decreasing

Hint:

For a short bar magnet, magnetic field is maximum on the axial line and minimum on the equatorial line for the same distance.

Answer 1

The Correct Option is D

Step 1: Magnetic field on axial line.
The magnetic field due to a short bar magnet on its axial line is given by \[ B_{\text{axial}} = \frac{2\mu_0 m}{4\pi r^3} \] This value is maximum for a given distance \( r \).
Step 2: Magnetic field on equatorial line.
On the equatorial line, the magnetic field is \[ B_{\text{equatorial}} = \frac{\mu_0 m}{4\pi r^3} \] which is half of the axial field.
Step 3: Movement along circular path.
As we move from the axial line towards the equatorial line along a circular path of fixed radius \( r \), the magnetic field continuously decreases from its axial value to its equatorial value.
Step 4: Conclusion.
Therefore, the magnetic field goes on decreasing.