Question

The conducting rod $ab$, as shown in figure makes contact with metal rails $ca$ and $db$. The apparatus is in a uniform magnetic field of $0.800T$, perpendicular to the plane of the figure. If the resistance of the circuit $abdc$ is $1.50\Omega$ (assumed to be constant), find the force (magnitude and direction) required to keep the rod moving to the right with a constant speed of $7.50m/s$. You can ignore friction.

Answer 1

$F=F_m=ilB=\frac{e}{r}\cdot lB=\frac{Bvl}{r}\cdot Bl=\frac{B^2{l}^2}{r}\cdot v$$=\frac{{\left(0.8\right)}^2{\left(0.5\right)}^2}{{\left(1.5\right)}^{}}\times 7.5=0.8N$