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

When a current carrying loop is placed in a magnetic field, the coil experiences a torque given by $\tau=N B i A \sin \theta$. Torque is maximum when $\theta=90^{\circ}$, i.e., the plane of the coil is parallel to the field $\tau_{\max }=N B i A$ Forces $\overrightarrow{ F }_{1}$ and $\overrightarrow{ F }_{2}$ acting on the coil are equal in magnitude and opposite in direction. As the forces $\overrightarrow{ F }_{1}$ and $\overrightarrow{ F }_{2}$ have the same line of action their resultant effect on the coil is zero. The two forces $\overrightarrow{ F }_{3}$ and $\overrightarrow{ F }_{4}$ are equal in magnitude and opposite in direction. As the two forces have different lines of action, they constitute a torque. Thus, if the force on one arc of the loop is $\overrightarrow{ F }$, the net force on the remaining three arms of the loop is $- \vec{F}$.