TS EAMCET · Physics · Magnetic Effects of Current

A wire of length \(l\) is bent into a circular loop of radius \(R\) and carries a current \(I\). The magnetic field at the centre of the loop is \(B\). The same wire is now bent into a double loop of equal radii. If both loops carry the same current \(I\) and it is in the same direction, the magnetic field at the centre of the double loop will be

A Zero
B 2 B
C 4 B
D 8 B

Verified Solution

Answer & Solution

Correct Answer

(A) Zero

Step-by-step Solution

Detailed explanation

Magnetic field at the centre of the loop \(B=\frac{\mu_0}{4 \pi} \cdot \frac{I \cdot 2 \pi R}{R^2}\).....(i) For the wire which is looped double let radius becomes \(r\) Then, \(\begin{aligned} \frac{l}{2} & =2 \pi r \\ \text{or} \quad \frac{l}{4 \pi} & =(r) \end{aligned}\)…

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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