CUET · PHYSICS · PYQ PAPER 2023

A square coil of side 10 cm, 500 turns and resistance 3 \(\Omega\) is placed with its plane perpendicular to the horizontal component of the Earth's magnetic field. It is rotated about vertical axis passing through centre by 180° in 0.25 second. Estimate the magnitude of the emf and current induced in the coil. Horizontal component of the Earth's magnetic field at the place is 3.0 \(\times 10^{-5}\) T.

A 9 \(\times 10^{-6}\) V, 3 \(\times 10^{-6}\) A
B 21 \(\times 10^{-6}\) V, 7 \(\times 10^{-6}\) A
C 12 \(\times 10^{-6}\) V, 4 \(\times 10^{-6}\) A
D 12 \(\times 10^{-4}\) V, 4 \(\times 10^{-4}\) A

Verified Solution

Answer & Solution

Correct Answer

(D) 12 \(\times 10^{-4}\) V, 4 \(\times 10^{-4}\) A

Step-by-step Solution

Detailed explanation

\(A = s^2 = (0.1)^2 = 0.01 \text{ m}^2\) \(\Delta\Phi = 2NBA = 2 \times 500 \times 3.0 \times 10^{-5} \times 0.01 = 3.0 \times 10^{-4} \text{ Wb}\) \(\epsilon = \frac{\Delta\Phi}{\Delta t} = \frac{3.0 \times 10^{-4}}{0.25} = 12 \times 10^{-4} \text{ V}\)…

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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