Question

A circular loop of wire, carrying a current 'I' is lying in the xy-plane with its centre coinciding with the origin. It is subjected to a uniform magnetic field pointing along the +z-axis. The loop will:

• A. move along the x-axis
• B. move along the y-axis
• C. move along the z-axis
• D. remain stationary

Hint:

When considering the motion of a current-carrying conductor in a magnetic field, always check for symmetry and the directions of \( \vec{B} \), \( \vec{dl} \), and the resultant \( \vec{dl} \times \vec{B} \). Symmetry often leads to cancellation of forces, especially in uniform fields.

Answer 1

The Correct Option is D

Step 1: Force Analysis on the Loop.
A current-carrying loop in a magnetic field experiences a force defined by \( \vec{F} = I(\vec{dl} \times \vec{B}) \), where \( \vec{dl} \) represents a loop segment and \( \vec{B} \) denotes the magnetic field. Here, \( \vec{B} \) is uniform along the +z-axis, and the loop is situated in the xy-plane.Step 2: Net Force Calculation.
Due to the loop's symmetry and the uniform field, opposing sides experience equal and opposite forces, resulting in cancellation of forces in the x and y directions. Vertical (z-axis) force components also cancel owing to symmetry and the alignment of the magnetic field and current.Step 3: Resultant Motion Determination.
With forces canceling, the loop experiences no net force. Absent any external torque causing rotation, the loop will exhibit neither translational nor rotational motion.