I am trying to explain this problem:
A circular conducting loop composed of N turns of wire has a radius of r and a total resistance of R. Perpendicular to the plane of the loop is a magnetic field of strength B. At what rate (in T/s) must this field change, if the induced current that flows in the loop is to be I?
So Faraday's law tells me that voltage is induced in a coil by a changing magnetic field.
emf = -N*B*A/t
And then I can solve for B/t and get
B/t = -emf/(N*A)
Easy, but what about the current? Everywhere around the internets, it's telling me to use Ohm's law to get
B/t = -R*I/(N*A)
And that certainly seems like what I'm supposed to do based on what I'm given in the problem. But that doesn't make sense to me because it's not a resistor; it's a coil, more like an inductor. Does it not store energy when current passes through it? Why don't I have to use the crazy formulae for voltage/current through an inductor with all the derivatives and such? Does the fact that it's closed have anything to do with it?
Please explain to me how is Ohm's law valid here.