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Let's say a current

*i(t)*flows through an inductor of solenoid type. Time-varying

*i(t)*generates a magnetic field

*B(t)*inside the magnetic core of the inductor. As

*B(t)*is time-varying, EMF, which is the line-integral of the induced electric field

*E(t)*along a coil (which carries

*i(t)*) around the core, is made (In fact, I'm not convinced yet that

*E(t)*is really to be called "induced" one, as there is no clue that

*E(t)*is "caused" by

*B(t)*in the Maxwell equation.

*E(t)*and

*B(t)*here are may be better called "dual". But for convience, I'll keep call it "induced").

**My question is why EMF has to be voltage applied on the inductor?**If EMF-field

*E(t)*is the only electric field present on the inductor coil, then EMF is deserved to be called a voltage. But...Is EMF-field only electric field existing on the coil? The current density is expressed as

*J = σE'*where

*σ*is the conductivity of the conductor. We know that voltage on the inductor and current flowing on it are not in-phase (there is actuall 90 degree phase differece between the volage and current on the inductor), so

*E'*is not necessarilly equal to EMF-fiedl

*E(t)*, I think. (If

*E' = E*, then voltage and current are in-phase, but it is not true in the inductor).

I thought EMF-field

*E*is so much larger than

*E'*in

*J = σE*in the inductor so that

*E'*can be ignored in the voltage calculation. But if this is true, the current should flows the same direction of

*E'*but this is not always true.

Thanks for reading this post I hope there would be some comments on this.