A conducting rod of mass \(m\) and length \(\ell\) is placed on two parallel, horizontal, frictionless conducting rails separated by a distance \(\ell\) in a uniform vertical magnetic field of magnitude \(B\). The rails are connected at one end to an ideal capacitor of capacitance \(C\), and the electrical resistance of the rails and rod is negligible. Starting from rest at time \(t = 0\), a constant external horizontal force \(F\) pulls the rod along the rails directed away from the capacitor. Which of the following statements correctly describes the motion of the rod in the limit as \(t \to \infty\)?