A conducting bar of length \(\ell\) and resistance \(R\) slides horizontally with negligible friction along two parallel conducting rails of negligible resistance separated by a distance \(\ell\). A uniform magnetic field \(\vec{B}\) of magnitude \(B\) is directed perpendicularly into the page, and an ideal battery of emf \(\mathcal{E}\) is connected across the left ends of the rails with its positive terminal at the top rail. An external agent pulls the bar to the right at a constant speed \(v\), where \(v > \dfrac{\mathcal{E}}{B\ell}\). What is the mechanical power supplied by the external agent to maintain this motion?