I'm struggling to conceptually understand the current-time profile of an RL circuit. Specifically, what causes the rate of change of current, $\frac{\partial i}{\partial t}$, to start off high when you first connect the battery and decrease with time?
I understand that the current through the inductor induces a magnetic field, $\vec{B}$, around the inductor which itself induces an emf, $\epsilon_L$, which acts to oppose the change in magnetic flux, $\phi_B$. This is a statement of Faraday's induction and Lenz's law.
To me, as soon as the battery is connected, the rate of change of current is at its maximum which means the induced emf across the inductor is at its maximum. is that right?
If it is, is it also correct to state that this reduces the rate of change in current and in so doing the induced emf decreases?
Would this not allow the current in the circuit to increase again?