Question

Find the in current in the conductor PQ so that it remains in equilibrium under its weight and the magnetic force. If direction of current is reversed then what would be the initial acceleration of the rod? Mass of the rod is m. (Friction is assumed to be absent)

Answer 1

Magnetic force on the conductor is equal to $F_m=BIl$. This force along horizontal. Direction of I should be from Q and P. In this case its component $F_{m}cos\theta$ will balance $mgsin\theta$ to keep it in equilibrium.
Since the rod can not move along perpendicular to the plane of the rails.
Hence for equilibrium $F_{m}cos\theta =mgsin\theta$
$\Rightarrow F_m=mgtan\theta$
$\Rightarrow BIl=mgtan\theta \Rightarrow I=mgtan\theta /bl$
On reversing the direction of current accleration of the rod will be

$a=\frac{F_{m}cos\theta +mgsin\theta }{m}=\frac{BIlcos\theta +mgsin\theta }{m}=2gsin\theta$