By Faraday's law of electromagnetic induction, the induced emf in an inductor is \(\mathcal{E} = -L\frac{dI}{dt}\). Rearranging: \(\frac{dI}{dt} = -\frac{\mathcal{E}}{L}\). So the rate of change of current is proportional to the negative of the induced emf (\(-\mathcal{E}\)). The negative sign (Lenz's law) indicates opposition to the change.