Question

A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is $\overrightarrow{F}$ .the net force on the remaining three arms of the loop is

• A. $3\vec{F}$
• B. $-\vec{F}$
• C. $-3\vec{F}$
• D. $\vec{F}$

Answer 1

The Correct Option is B

To solve this problem, we need to understand the concept of forces on a current-carrying loop within a magnetic field. A square loop with current represents a magnetic dipole, and according to physics principles, particularly those concerning torque and magnetic forces, a loop in a magnetic field experiences forces distributed along its arms.

Given that the force on one arm of the loop is $\overrightarrow{F}$, we are tasked with finding the net force on the remaining three arms of the loop.

1. Each side of the square loop carries current and when suspended in a magnetic field within its plane, each side of the loop experiences forces.
2. The magnetic force on a current-carrying wire in a magnetic field can be given by the formula: $\overrightarrow{F} = I (\overrightarrow{L} \times \overrightarrow{B})$ where $I$ is current, $\overrightarrow{L}$ is the length vector of the arm, and $ \overrightarrow{B}$ is the magnetic field.
3. As the magnetic field is in the plane of the loop, the net force acting on the closed loop should be zero for the loop to remain stable or in equilibrium.
4. Therefore, if one arm experiences a force $\overrightarrow{F}$, to maintain equilibrium, the remaining three arms must exert a force that is equal in magnitude and opposite in direction, i.e., $-\overrightarrow{F}$ as the net force on the loop should be zero.

Hence, the correct option is $-\vec{F}$, indicating that the net force on the remaining three arms of the loop is of equal magnitude but opposite direction to ensure equilibrium.