Question

A loop carrying a current I clockwise is placed in x - y plane, in a uniform magnetic field directed along z-axis. The tendency of the loop will be to:

• A. move along x-axis
• B. move along y-axis
• C. shrink
• D. expand

Hint:

When a current carrying loop lies in a plane perpendicular to a uniform magnetic field, the magnetic forces on the loop segments act radially outward. This produces a tendency for the loop to expand.

Answer 1

The Correct Option is D

Step 1: Direction of magnetic field and current.
The current carrying loop lies in the x–y plane and the magnetic field is directed along the z-axis. The current in the loop is clockwise. According to the right-hand rule, the magnetic forces acting on different segments of the loop must be analyzed using the Lorentz force law.
Step 2: Magnetic force on a current element.
The force on a current carrying conductor in a magnetic field is given by \[ \vec{F} = I (\vec{L} \times \vec{B}) \] where \(I\) is the current, \(\vec{L}\) is the length vector in the direction of current, and \(\vec{B}\) is the magnetic field.
Step 3: Direction of forces on the loop segments.
Each segment of the loop experiences a force due to the magnetic field. Because the magnetic field is perpendicular to the plane of the loop, the forces on all the sides of the loop act radially outward. This happens due to the cross product \( \vec{L} \times \vec{B} \). Thus every small segment of the loop experiences a force directed away from the center.
Step 4: Resulting effect on the loop.
Since the forces on all parts of the loop are directed outward, the loop experiences a tendency to increase its area. Therefore, the loop tends to expand rather than move along the x-axis or y-axis.
Final Answer: expand.