Two concentric rings are kept in the same plane. Number of turns in each sign is 25 . Their radii are 50 cm and 200 cm and they carry electric currents of 0.1 A and 0.2 A respectively in mutually opposite directions. The magnitude of the magnetic field produced at their centre is _________ T.

A \(4 \mu_0\)
B \(2 \mu_0\)
C \(\frac{10}{4} \mu_0\)
D \(\frac{5}{4} \mu_0\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{5}{4} \mu_0\)

Step-by-step Solution

Detailed explanation

D
From \(\quad B _{\text {centre }}=\frac{\mu_0 N I }{2 a}\)
\(B \quad= B _1- B _2\)
\(\begin{array}{ll}\therefore B=\frac{\mu_0 N}{2}\left[\frac{I_1}{a_1}-\frac{I_2}{a_2}\right] \\ \therefore B=\frac{\mu_0 \times 25}{2}\left[\frac{0.1}{0.5}-\frac{0.2}{2}\right] \\ \therefore B=\frac{\mu_0 \times 25}{2}\left[\frac{1}{5}-\frac{1}{10}\right] \\ \therefore B=\frac{\mu_0 \times 25}{2}\left[\frac{1}{10}\right] \\ \therefore B=\frac{5}{4} \mu_0\end{array}\)

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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