Question #43398

A U-shaped conducting frame with parallel rails separated by a distance $L$ is fixed on an inclined plane of angle $\theta$. The rails are connected at the top by a resistor of resistance $R_0$. A conducting rod of mass $m$ can slide down the rails. The coefficient of kinetic friction between the rod and the rails is $\mu$. Let the incline surface define the $x-z$ plane, with the $x$-axis pointing directly down the incline and the $z$-axis horizontal. The top edge of the frame lies on the $z$-axis ($x=0$). The $y$-axis is perpendicular to the incline, pointing upwards. An infinitely long straight wire carrying a constant current $I$ in the $+z$ direction is fixed parallel to the $z$-axis at a position $(x=0, y=-d)$. The rod is pulled down the incline at a constant velocity $v$ by an external force. Assuming the resistance of the rod and rails is negligible, find the magnitude of the total resistive force (sum of kinetic friction and magnetic drag) acting on the rod when it is at a distance $x$ down the incline.