Question

A wire $ABCDEF$ (with each side of length $L$ ) bent as shown in figure and carrying a current $I$ is placed in uniform magnetic field $\vec{B}$ parallel to the positive $y$ direction. The force experienced by the wire in the direction is

• A. $2BIL\hat{k}$
• B. $\frac{BIL}{2}\hat{k}$
• C. $BIL\hat{k}$
• D. $\frac{BIL}{4}\hat{k}$

Answer 1

Answer: (C)

The magnetic field $\vec{B}=B\hat{j}$. So, the conductors $FE$ and $BA$ are parallel to the magnetic field. These conductors will not experience any force at all. On the other hand, the force on $CB$ is +ve in $x$ -direction and that on $ED$ is in $-$ ve $x$ -direction. So, the forces will cancel each other. The force on the remaining portion $DC$ is $(BIL)\hat{k}.$