CUET · PHYSICS · PYQ PAPER 2023

Two conducting circular loops of radii a and b are placed in the same plane with their centre coinciding. If \( a \gg b \), the mutual inductance M between then will be directly proportional to:

A \(\frac{a^2}{b}\)
B \(\frac{a}{b}\)
C \(\frac{b}{a}\)
D \(\frac{b^2}{a}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{b^2}{a}\)

Step-by-step Solution

Detailed explanation

The magnetic field produced at the center by a current \(I\) in the larger loop (radius \(a\) ) is \(B=\frac{\mu_0 I}{2 a}\). Since \(a \gg b\), the flux through the smaller loop is \(\phi = B \times\) Area \(=\left(\frac{\mu_0 I}{2 a}\right)\left(\pi b^2\right)\), which shows…

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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