Question

A conductor $ABCDEF$, shaped as shown, carries a current i. It is placed in the $xy$ plane with the ends $A$ and $E$ on the x-axis. A uniform magnetic field of magnitude $B$ exists in the region. The force acting on it will be :

• A. zero, if $B$ is in the $x-$direction
• B. $\lambda Bi$ in the $z-$direction, if $B$ is in the $y-$direction
• C. $\lambda Bi$ in the negative $y-$direction, if $B$ is in the $z-$direction
• D. $2aBi$, if $B$ is in the $x-$direction

Answer 1

Answer: (A), (B), (C)

The correct options are
A zero, if $B$ is in the $x-$direction
B $\lambda Bi$ in the $z-$direction, if $B$ is in the $y-$direction
C $\lambda Bi$ in the negative $y-$direction, if $B$ is in the $z-$direction

Replace the conductor by an imaginary straight conductor joining the two ends of the given conductor. Hence, if B is in X-direction, then imaginary straight conductor will be along the field and force acting on it will be zero.
If B is in Y-direction, then force will be $F=LBi=\lambda Bi$, acting along Z-direction. (Here L is the length between the end points of the conductor i.e AE=$\lambda$)
If B is in Z-direction, then force will be $F=LBi=\lambda Bi$, acting along the negative Y-direction.