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I'm pretty sure this has been answered somewhere around here.

So, consider a pure inductance (zero resistance) connected in series to a battery. We know that the magnitude of the induced voltage across the inductor is given by

[itex]E=L\normalsize[/itex][itex]\frac{di}{dt}[/itex].

According to KVL, the sum of the voltage drops must equal the sum of the source emfs, so according to the equation, the current in this circuit must increase at a rate such that the induced electromotive force constantly equals the battery voltage. Now with respect to polarity, if the applied voltage across the inductor is positive then the polarity of the induced emf is negative. All of this, I think I understand...correct me here if anything is wrong.

What I'm not understanding is this. If the induced voltage across the inductor is always equal and opposite the source emf, how can there possibly be a current at all? If there is no difference in electric potential, how can there be any work done?