A thin, uniform conducting disk of radius \(R\) rotates in the \(xy\)-plane about a fixed vertical axis through its center with a constant angular speed \(\omega\). A non-uniform magnetic field perpendicular to the plane of the disk is given by \(\vec{B}(r) = B_0 \left(\dfrac{r}{R}\right)^2 \hat{k}\), where \(r\) is the radial distance from the axis of rotation and \(B_0\) is a positive constant. Which of the following expressions represents the magnitude of the induced electromotive force (EMF) between the center of the disk and its outer rim?