The earth's magnetic field at the geometric poles is \(\sqrt{10} \times 10^5 \mathrm{~T}\). The magnitude of the field at a point on the earth's surface where the radius makes an angle \(\theta\) with the axis of earth's assumed magnetic dipole is \(5 \times 10^5 \mathrm{~T}\). The magnitude of \(\theta\) in degree is :

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.