A thin, straight conducting rod of length \(L\) is pivoted at one end and rotates with a constant angular speed \(\omega\) in a plane perpendicular to a magnetic field. The magnetic field is directed into the page and has a non-uniform magnitude that varies with the distance \(r\) from the pivot according to \(B(r) = B_0 \left(1 + \dfrac{r}{L}\right)\), where \(B_0\) is a positive constant. Which of the following expressions represents the magnitude of the induced electromotive force \(\mathcal{E}\) between the two ends of the rod?