Question

A wire loop with current I is placed in a uniform magnetic field. Which statement(s) are true about the wire loop? The net force is zero, but the net torque is not. There are no forces exerted on the current loop. The net force is zero. The loop will rotate.

Answer 1

1) The net force is zero, but the net torque is not (FALSE): The net force and the net torque are both zero.

2) There are no forces exerted on the current loop (FALSE): There are forces exerted on the current loop, which are given by the equation,

$\vec{F}_{m}=I\Delta \vec{L}\times \vec{B}$

3) The net force is zero ${\color{Blue} (TRUE)}$ : The net force is

$\vec{F}_{net}=\vec{F}_{right}+\vec{F}_{left}+\vec{F}_{top}+\vec{F}_{bottom}$

since,

$\vec{F}_{right}=-\vec{F}_{left}$

$\vec{F}_{top}=-\vec{F}_{bottom}$

we have,

$\vec{F}_{net}=\mathbf{0}$

4) The loop will rotate (FALSE): The net torque in the loop must be not zero to rotate, but the net torque is zero.

$\vec{\tau }_{net}=\vec{\tau }_{left}+\vec{\tau }_{right}+\vec{\tau }_{top}+\vec{\tau }_{bottom}$

$\vec{\tau }_{net}=rF _{left}(\sin 180^{\circ})+rF _{right}(\sin 180^{\circ})+0(F_{bottom})+0(F_{top})=\mathbf{0}$