Question

A conducting rod of length $l$ and mass $m$ is moving down a smooth inclined plane of inclination$\theta$ with constant velocity $v$. A current $i$ is flowing in the conductor in a direction perpendicular to paper inwards , a vertically upwards magnetic field $B$ exists in space. Then magnitude of magnetic field $B$ is :

• A. $\frac{mg}{il}sin\theta$
• B. $\frac{mg}{il}tan\theta$
• C. $\frac{mgcos\theta }{il}$
• D. $\frac{mg}{ilsin\theta }$

Answer 1

The correct option is B $\frac{mg}{il}tan\theta$

Magnetic force acts in the direction shown
Rod will move downward with constant velocity if net force on it is zero
$F_m\cos \theta =mg\sin \theta orilB\cos \theta =mg\sin \theta \therefore B=\left(\frac{mg}{il}\right)\tan \theta$