In which direction, the magnetic field on the axis at a distance \(Z\) from the centre of the bar magnet would be ?

A In the direction of the magnetic dipole moment ( \(\overrightarrow{ M }\) ) of the magnet.
B In the opposite direction of the magnetic dipole moment ( \(\overrightarrow{ M }\) ) of the magnet.
C In the perpendicular direction of the magnetic moment ( \(\overrightarrow{ M }\) ) of the magnet.
D Its direction depends on the magnitude of the magnetic moment \((\vec{M})\) of the magnet.

Verified Solution

Answer & Solution

Correct Answer

(A) In the direction of the magnetic dipole moment ( \(\overrightarrow{ M }\) ) of the magnet.

Step-by-step Solution

Detailed explanation

A
Magnetic field on axis will be in direction of dipole moment as per
\(\overrightarrow{ B }=\frac{\mu_0}{4 \pi} \frac{2 m}{z^3} \hat{m}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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