A conducting bar of length \(L\) slides to the right with constant speed \(v\) along two parallel conducting rails in a region of uniform magnetic field of magnitude \(B\) directed perpendicular to the plane of the rails. In steady state, charges within the moving bar separate until dynamic equilibrium is reached. Which of the following correctly pairs the magnitude of the induced electromotive force \(\mathcal{E}\) across the bar with the magnitude of the electric field \(E\) inside the bar?