A short bar magnet of magnetic moment \(0.21 \mathrm{~A}-\mathrm{m}^2\) is placed with its axis perpendicular to the direction of the horizontal component of the earth's magnetic field. The distance of the point on the axis of the magnet from the centre of the magnet where the resultant magnetic field is inclined at \(45^{\circ}\) with the horizontal component of the earth's field direction is (horizontal component of the earth's magnetic field \(=4.2 \times 10^{-5} \mathrm{~T}\) )

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.