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Question #43537

Difficulty: 8/10 | 🟢 Free

The Question

A thin, flexible insulating ring of radius $R$ and cross-sectional area $A$ has a uniform linear mass density $\lambda$ and a uniform positive linear charge density $\mu$ . The ring is rotated about its central axis, which is perpendicular to its plane, with a constant angular velocity $\omega$ . A uniform magnetic field of magnitude $B$ is applied parallel to the axis of rotation such that the resulting Lorentz force acts radially outward. If the material of the ring has a breaking stress $\sigma_b$ , which of the following expressions gives the minimum magnetic field $B$ required to break the ring? (Assume the ring remains perfectly circular until it breaks and neglect gravity).

Options

A.
$\frac{\sigma_b A}{\mu \omega R^2} - \frac{\lambda \omega}{\mu}$
B.
$\frac{\sigma_b A}{\mu \omega R^2}$
C.
$\frac{\sigma_b A}{\mu \omega R^2} + \frac{\lambda \omega}{\mu}$
D.
$\frac{2\sigma_b A}{\mu \omega R^2} - \frac{\lambda \omega}{\mu}$

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

Breaking Stress Concept|Force on Current-Carrying Loop|Vector Cross-Product

Why This Question Is Tricky

Common Mistakes

This question tests the superposition of mechanical and electromagnetic forces in determining structural equilibrium (Hoop Stress).

The primary trap lies in the calculation of the equivalent current of a rotating charged ring; students often incorrectly use $I = \mu \omega$ instead of $I = \mu \omega R$ , leading to dimensional inconsistencies.

Additionally, students frequently fail to account for the non-electromagnetic centrifugal force acting simultaneously on the mass of the ring, or they misapply the differential force balance $T d\theta = dF_{radial}$ by integrating over the entire loop and incorrectly concluding the net force (and thus tension) is zero.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Mechanical Properties of Solids - Class 11 Part 2
Concept	Breaking Stress Concept
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free