In a particular case \(X\), a certain length of insulated copper wire is bent to form double loops of equal radii. In another case Y the same copper wire is bent to form three loops of equal radii. If the same steady current is passed through the copper wire in both the cases, the ratio of magnetic field at the centre in the case X to that in case Y 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.