Question #42437

A uniform conducting rod of mass $m = 0.14 \text{ kg}$ and length $L = 0.5 \text{ m}$ rests symmetrically on two parallel, rough horizontal rails separated by a distance $L$. The rails are parallel to the y-axis and the rod is parallel to the x-axis. A uniform magnetic field $\vec{B} = B_0 (3\hat{i} + 4\hat{j} + 5\hat{k})$ exists in the region, where $B_0 = 0.1 \text{ T}$. The coefficient of static friction between the rod and the rails is $\mu = 0.5$. If a current $I$ is passed through the rod in the $+x$ direction, what is the minimum current $I$ required to just initiate sliding of the rod? (Take $g = 10 \text{ m/s}^2$)