A wire of length \(l\) is bent into a circular coil of one turn of radius \(R_1\). Another wire of the same material and same area of cross-section and same lengths is bent into a circular coil of two turns of radius \(R_2\). When the same current flows, through the two coils, the ratio of magnetic induction at the centres of the two coils 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.