MHT CET · Physics · Magnetic Effects of Current

A long wire carries a steady current. It is bent into a cirde of one turn and the magnetic field at the centre of the coil is \(B\). It is then bent into a circular loop of \(n\) turns. The magnetic field at the centre of the coil for same current will be

A \(n B\)
B \(n^{2} B\)
C \(2 n B\)
D \(2 n^{2} B\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(n^{2} B\)

Step-by-step Solution

Detailed explanation

Magnetic field at the centre of single turn loop \(B=\frac{\mu_{0}}{4 \pi} \frac{2 \pi I}{r}\), magnetic field at the centre of \(n\) turn loop
\(B_{n}=\left[\frac{\mu_{0}}{4 \pi} \frac{2 \pi I}{r / n}\right] \times n\)
\(\Rightarrow B_{n}=n^{2} B\)

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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