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Let's say a currenti(t)flows through an inductor of solenoid type. Time-varyingi(t)generates a magnetic fieldB(t)inside the magnetic core of the inductor. AsB(t)is time-varying, EMF, which is the line-integral of the induced electric fieldE(t)along a coil (which carriesi(t)) around the core, is made (In fact, I'm not convinced yet thatE(t)is really to be called "induced" one, as there is no clue thatE(t)is "caused" byB(t)in the Maxwell equation.E(t)andB(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-fieldE(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 asJ = σE'whereσis 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), soE'is not necessarilly equal to EMF-fiedlE(t), I think. (IfE' = E, then voltage and current are in-phase, but it is not true in the inductor).

I thought EMF-fieldEis so much larger thanE'inJ = σEin the inductor so thatE'can be ignored in the voltage calculation. But if this is true, the current should flows the same direction ofE'but this is not always true.

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

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# Why is EMF (ElectroMotive Force) equal to a voltage?

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