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A circular coil of radius A surrounds a cylindrical, infinitely tall, uniform magnetic field pointed upwards, of radius B. A>B, and both are centered on the same point. The field is steadily increase in strength, but the constrained area stays the same. Will a current be induced in the wire?

The flux is increasing, yes, but at the wire itself, there is no changing magnetic field because the magnetic field is constrained to a smaller area. Does using magnetic flux not work to explain this problem? How could the loop be affected? My teacher says it is, because of the flux. My theory is it isn't, because it wouldn't be consider an enclosed circle, because of the gap between the flux and the wire. Can anyone explain?

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  • $\begingroup$ Even if magnetic field is constrained to a small area, any change in it will cause a current so as to oppose the change of magnetic field (this is called Lenz Law). $\endgroup$
    – user102705
    Feb 7, 2017 at 18:29
  • $\begingroup$ Even if the field isn't actually affecting the coil itself? How are the electrons "feeling" the force of a field they're not in? $\endgroup$
    – Your Mom
    Feb 7, 2017 at 19:10
  • $\begingroup$ 1) The field is affecting the coil. 2) The electrons respond to any change in magnetic field or more specifically magnetic flux. Please read up Lenz law and Faraday's law of EM induction from Wikipedia or some textbook. $\endgroup$
    – user102705
    Feb 7, 2017 at 19:14
  • $\begingroup$ I know lentz's law, and I understand how it interacts with a coil that's in a uniform magnetic field completely or partially. How does a the field cause a reverse field in a coil that it isn't affecting? For example, in an extreme case, say the field from a planet 10 light years away is massive, 10^10000T, but doesn't actually reach the earth, it stops due to some unknown barrier around that planet. Would a coil on our planet be affected by it, despite the field stopping 10 light years away? $\endgroup$
    – Your Mom
    Feb 7, 2017 at 20:42

1 Answer 1

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A changing magnetic flux induces an emf , which in turn gives rise to a current in a wire. Note this statement, for I shall use it later to explain my answer. Here the field that you have mentioned, changes with time not space. Let the field at any instant t be Ct and the area to which it is constrained be $πx^2$.Now, according to your problem the circular coil has a radius R>x. So there is a gap between the coil and the field which is causing your intuition trouble.

But you see, it does not matter whether there is a gap or not. An emf is always induced along a surface if the flux linked with it is changing. Although it may seem weird, but the emf is induced irrespective of whether there is a wire or not, as the field is changing with time . In case of field changing with time, if you consider any surface which contains even a bit of this changing field then the flux linked with it changes and an emf is induced. Your circular coil contains this entire changing field and the flux linked with its area is changing with time. That is all an emf needs to be induced. And it is not the magnetic field but the changing magnetic flux which gives rise to an electric field which makes the electrons move.

It would help allay your confusion once you realize that emf and current are two completely different things. Current needs an emf as well as a material with free electrons(conductor). Your traditional view of electromagnetic induction is a magnetic field encompassing a closed circuit, whose value changes with space and hence flux changes with time and an induced emf gives rise to current in the wire. But even if you had an insulator, Faraday's Law would hold.No current will flow due to no free electrons being present( just like connecting a battery to an insulator; nothing happens) but the emf will still be there.

So, flux linked with your coil is $Cπx^2t$ which changes with time and gives you the induced emf as $Cπx^2$. Thus, it all comes down to whether the flux linked is changing with time or not. And this happens with your coil, as the field is within its area.

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