COMEDK · Physics · 21. Magnetic Effects of Current

A straight wire carrying current of 21 A is bent into an arc of radius 11 cm as shown below. The magnetic field produced by the current at the centre \(O\) of the arc is:

A \(3.0 \times 10^{-4} \mathrm{~T}\)
B \(3.0 \times 10^{-3} \mathrm{~T}\)
C \(0.3 \times 10^{-5} \mathrm{~T}\)
D \(0.3 \times 10^{-4} \mathrm{~T}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(0.3 \times 10^{-4} \mathrm{~T}\)

Step-by-step Solution

Detailed explanation

The straight segments pass through centre \(O\), so they produce no magnetic field at \(O\). The arc is a quarter circle, so \(\theta = \dfrac{\pi}{2}\) \(B = \dfrac{\mu_0 I}{4\pi r} \cdot \theta = \dfrac{\mu_0 I}{4\pi r} \cdot \dfrac{\pi}{2} = \dfrac{\mu_0 I}{8r}\)…

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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