Resistive long-time drift of an inductive sliding rod ($v_{\infty }=Rmg\sin \theta /(B^2{l}^2{\cos }^2\theta )$)

For positive loop resistance, coupled mechanical and circuit equations relax toward constant sliding speed on sufficiently long rails. The steady current balances the downhill gravitational force, and motional electromotive force balances the resistive voltage. The undamped zero-resistance limit has no relaxation, so its late-time limit is singular.