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Question #43345

Difficulty: 8/10 | 🟢 Free

The Question

A superconducting circular loop of area $A$ , self-inductance $L$ , and moment of inertia $I_m$ about its diameter is placed in a uniform magnetic field of induction $B$ . Initially, the loop is held at rest such that its area vector makes an angle $\theta = \pi/2$ with the direction of the magnetic field. The initial current in the loop is $I_0 = \frac{2BA}{L}$ . The loop is then released and is free to rotate about a diameter perpendicular to the magnetic field. Assuming no energy is lost to radiation or friction, what is the maximum angular velocity $\omega$ of the loop during its subsequent motion?

Options

A.
$BA \sqrt{\frac{3}{L I_m}}$
B.
$BA \sqrt{\frac{5}{L I_m}}$
C.
$2BA \sqrt{\frac{1}{L I_m}}$
D.
$BA \sqrt{\frac{1}{L I_m}}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

LC Oscillations Energy Cycle|Magnetic Dipole Moment Orientation|Vector Cross-Product

Why This Question Is Tricky

Common Mistakes

This question tests the subtle distinction between the energy of a constant-current dipole and a constant-flux (superconducting) loop.

Students often incorrectly apply the potential energy formula $U = -\vec{\mu}\cdot\vec{B}$ alongside the self-energy $\frac{1}{2}LI^2$ , leading to double-counting of the interaction energy.

For a superconducting loop, flux is conserved, and the system is isolated; the work done by the external magnetic field on the loop is entirely reflected in the variation of the internal magnetic energy $\frac{1}{2}LI^2$ .

The trap option B is obtained if the $-\vec{\mu}\cdot\vec{B}$ term is erroneously included in the energy conservation equation, while option C assumes the current remains constant during rotation.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Alternating Current - Class 12
Concept	LC Oscillations Energy Cycle
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free