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If magnetic field is increased at a constant rate inside a zero resistance wire loop,

then, according to Faraday's law ,

$$\varepsilon = \frac{dΦ}{dt} $$

Thus, a potential difference is produced.

Also, according to Kirchhoff's law, net $\varepsilon$ in a loop is $0$. So, in short it says the changing flux doesn't produce any emf in the loop.

Both these laws are understandable when it's a simple circuit or even a superconducting circuit with a battery. But in this case these 2 laws seem contradicting. It may happen that either of the laws don't apply in extreme conditions like in a superconductor. Can somebody help?

I have read this post : Superconducting wire in a Magnetic Field? But it asks about a straight wire and not a loop. Also, it is not answered well (or at least i didn't understand much out of it).

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Shubham
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2 Answers2

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The first sentence started with an if. When you start with an if and end with a problem a solution you should consider is that your if never happens.

So if the EMF around a zero resistance loop is zero then we don't expect the total magnetic flux through to change. Is that reasonable? Yes. Since it is a zero resistance loop, it can generate any current it needs, including the exact current that cancels the change in magnetic flux that other sources besides the loop would make.

Induced currents also make a contribution to the magnetic field that makes the flux change less than it otherwise would (Lenz's law). A zero resistance wire can do an excellent job.

for that exact current to get produced don't you need an emf produced first ?

An EMF is needed to supply power to overcome resistance, there is no resistance. For wires without resistance you have to figure out what makes there be current. Its energy and momentum balance, so you'd have to track the flow of energy and momentum from the fields to the charges and currents.

It would help if you were more detailed about an experimental setup. Like placed a loop inside a solenoid and make the solenoid increase its current according to your will. This won't be the only source of magnetic field, so you can't make there be the flux you want through that zero resistance loop.

Timaeus
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I agree with the above. The instant you attempt to change the flux linking a loop of zero resistance, an opposing induced magnetic field would immediately negate the attempted change of flux (according to Lenz’s Law). In other words, it is not possible to change the flux linking a zero resistance loop. A similar thing is true if you are moving a straight wire of zero resistance through a magnetic field.A current and magnetic field would be induced which would instantly cancel out the local external field.

Roger
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