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I was recently helping a friend of mine with a fairly standard electromagnetic induction problem (a basic sketch of the set-up is attached) where we have a current loop with resistance ##R## moving through a magnetic dipole and had to roughly sketch out the current induced in the loop due to Faraday's law. The reason we are able to do this is because Faraday's law will tell us the EMF induced in the loop, and Ohm's law, ##ε = IR##, will let us find the current from that.

However, later that day, I began to think to myself: what if the resistance around the current loop is zero? The current loop is then an ideal conductor, and we are taught that the potential difference across an ideal conductor is zero. However, if we then look back at Faraday's law,

##\oint \vec E \cdot d \vec l = -\frac {d} {dt}\iint \vec B \cdot d \vec A##

We see that no where does the induction of the EMF depend upon the resistance of the loop, and that it only depends upon there being a changing magnetic flux density through the loop. However, if we assume we get an EMF around the loop, then we should have a current in the loop due to the existence of an electric field. In that case, the induced current should create its own magnetic field through the loop. Since there is no resistance in the loop, intuitively I would think that current could flow "freely" and create a magnetic field that would exactly "cancel out" the magnetic field due to the dipole and result in no net flux in the loop. This then means, due to Faraday's law, that the EMF in the loop should then be zero.

Is my line of reasoning correct here within the realm of classical electrodynamics? Or am I missing something?

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# I Faraday's Law with Zero Resistance Current Loop

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