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Question #43399

Difficulty: 8/10 | 🟢 Free

The Question

A rigid square loop of side $a$ and mass $m$ lies flat on a rough horizontal table. The coefficient of static friction between the loop and the table is $\mu$ . A long straight wire is fixed horizontally at a height $a$ directly above the left edge of the loop. The long wire carries a steady current $I_1$ . The loop carries a steady current $I_2$ in such a direction that the magnetic force on its left edge is directed downwards. As the product $I_1 I_2$ is gradually increased from zero, what is the condition on $\mu$ such that the loop topples about its left edge before it starts sliding?

Options

A.
$\mu > \frac{1}{3}$
B.
$\mu > \frac{1}{2}$
C.
$\mu > \frac{2}{3}$
D.
$\mu > \frac{1}{4}$

Check Your Answer

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

Infinite Wire vs. Finite Wire|Toppling vs Sliding|Moment of Inertia (MOI) Symmetry

Why This Question Is Tricky

Common Mistakes

This problem tests the integration of magnetic forces in a highly non-uniform field and the rigid body dynamics of toppling versus sliding.

A primary trap is assuming the normal force remains $mg$ , ignoring the net downward magnetic force caused by the field gradient.

If students incorrectly use $N=mg$ , they will find the erroneous condition $\mu > 1/2$ .

Additionally, students might attempt to use a dipole approximation ( $\vec{\tau} = \vec{M} \times \vec{B}$ ) which is completely invalid here because the magnetic field varies significantly in both magnitude and direction across the loop's dimensions.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Infinite Wire vs. Finite Wire
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free