CUET · PHYSICS · PYQ PAPER 2023

An insulating rod of length \( L \) carries charge \( q \) distributed uniformly on it. The rod is pivoted at one end and is rotated at a frequency \( f \) about a fixed perpendicular axis. Then the magnetic dipole moment of the system is :

A \( \pi q f L^2 \)
B \( \frac{1}{3} \pi q f L^2 \)
C \( q f L \)
D \( q f L^2 \)

Verified Solution

Answer & Solution

Correct Answer

(B) \( \frac{1}{3} \pi q f L^2 \)

Step-by-step Solution

Detailed explanation

\( dq = \frac{q}{L} dx \) \( d\mu = \pi (dq) f x^2 = \frac{\pi q f}{L} x^2 dx \) \( \mu = \int_{0}^{L} \frac{\pi q f}{L} x^2 dx = \frac{\pi q f}{L} \left[ \frac{x^3}{3} \right]_{0}^{L} = \frac{1}{3} \pi q f L^2 \)

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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List - I	List - II
(A) Interference experiment	(I) Maxwell
(B) Electromagnetic theory of light	(II) Christian Huygens
(C) Wave theory of light	(III) Isaac Newton
(D) Particle theory of light	(IV) Thomas Young