Question

In a trapeze-shaped structure, two rigid wires of negligible mass support a conducting bar of mass m and length L as shown in fig. A source of emf is applied to the wires so that a current I flows through the bar. A uniform magnetic field $\overrightarrow{B}$ is perpendicular to the plane of the wires and bar.
If the current is reduced to half the value computed in (a) and the place of the structure is moved through an angle $\theta$, compute the tension in the wires and the magnitude of the net unbalanced force on the bar at the instant it is released from this angle

Answer 1

If the wires is in equilibrium, the forces acting on it are as shown in fig.
$i=\frac{mg}{2LB}\therefore F_B=\frac{1}{2}mg$
For tension in the wire, $2T+F_{B}cos\theta =mgcos\theta$
$T=\frac{mg}{4}cos\theta$
Net unbalanced force on the rod will be in the direction perpendicular to the wire
$F_{net}=mgsin\theta -F_{B}sin\theta$
$F_{net}=\frac{mg}{2}cos\theta$