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Question #43861

Difficulty: 8/10 | 🟢 Free

The Question

A flexible, uniform circular wire loop of radius $R$ and linear mass density $\mu$ carries a steady current $I$ . The loop is placed in a uniform magnetic field of magnitude $B$ directed perpendicular to the plane of the loop, such that the Lorentz force tends to expand the loop radially outward. The loop is simultaneously rotating about its central axis (which is parallel to the magnetic field) with a constant angular velocity $\omega$ . A small transverse wave pulse, which displaces the wire perpendicular to its plane, is generated at a point on the wire. What is the time $t$ taken by this wave pulse, traveling in the direction of the loop's rotation, to complete exactly one full revolution around the loop as observed from a stationary laboratory frame?

Options

A.
$\frac{2\pi R}{\sqrt{\frac{I R B}{\mu} + \omega^2 R^2} + \omega R}$
B.
$\frac{2\pi R}{\sqrt{\frac{I R B}{\mu}} + \omega R}$
C.
$\frac{2\pi R}{\sqrt{\frac{I R B}{\mu} + \omega^2 R^2}}$
D.
$\frac{2\pi R}{\sqrt{\frac{I R B}{\mu} - \omega^2 R^2} + \omega R}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

String Tension and Wave Speed|Force on Current-Carrying Loop|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the coupling of electromagnetism and classical wave mechanics in a rotating reference frame.

The primary trap lies in the calculation of the tension $T$ in the wire.

Students often correctly identify the magnetic tension $T_m = IRB$ derived from the Lorentz force but fail to account for the mechanical tension $T_c = \mu \omega^2 R^2$ required to provide the centripetal acceleration for the rotating mass of the wire.

A secondary trap is the Galilean velocity addition; students might calculate the wave speed relative to the wire but forget to add the tangential velocity of the medium ( $\omega R$ ) when determining the time taken in the stationary laboratory frame.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Waves - Class 11 Part 2
Concept	String Tension and Wave Speed
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free