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Consider a circular loop kept in a time-changing magnetic field. We know, via Faraday Law, that EMF is induced across the loop and hence a current appears in the loop. Let there be some Resistance given in the wire. Then heat will appear in the circuit.

How does heat energy appear in the circuit?

I know that an electric field is generated by a changing magnetic field and my guess is that this generated electric field contains some energy which finally appears as heat. But I am unsure about it.

This is because I know the induced electric field does not have a potential associated with it. So what form of energy is stored in this field, if any?

Please provide an explanation as to :

From where does heat appear in the loop?

If possible please start the energy considerations right from the source which produces the varying magnetic field.

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    $\begingroup$ This is because I know the induced electric field does not have a potential associated with it. It's a barrier to learning when know something that isn't true. There is a potential associated with a changing magnetic field, it's just that it's a rather unusual multi-valued potential, which increases each time you go round a loop surrounding the changing field. $\endgroup$
    – Neil_UK
    Commented Aug 29, 2020 at 21:31
  • $\begingroup$ @Neil_UK Is it something like this - each time I go around the loop, the potential is regenerated? Further if I do not place any loop, the potential remains constant (given Magnetic field varies linearly) ? $\endgroup$
    – Tony Stark
    Commented Aug 30, 2020 at 2:29
  • $\begingroup$ The potential is not regenerated, the potential continually increases as you progress round the loop. Unfortunately, the best way to describe potential is change of energy as you move charge, and that's precisely the thing you're having trouble with. Consider a transformer, a 10 turn secondary generates 10x the total voltage that a 1 turn secondary does. If you do not place a loop? The loop is there, topologically, it doesn't matter whether you physically place a conductor there or not, see the Betatron $\endgroup$
    – Neil_UK
    Commented Aug 30, 2020 at 4:35
  • $\begingroup$ @Neil_UK In case it is not too much trouble,do you mind writing a proper answer as by far you have interpreted my question best, $\endgroup$
    – Tony Stark
    Commented Aug 30, 2020 at 5:21
  • $\begingroup$ How and why are not really questions that physics can answer. When we observe something, like a wire looped round a changing magnetic field gets hot, we then devise models to predict what will happen. The models have to be consistent with the observation. Potential is a 'book keeping' thing that helps us keep account of how the energy of a test charge varies as we take it round the loop, nothing more. Because the energy rises with every once around the loop, the potential, or pseudo-potential as it's sometimes called, has to be multi-valued. How energy gets from field to wire? QED may? $\endgroup$
    – Neil_UK
    Commented Aug 30, 2020 at 15:08

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The heat comes from current flowing through the wire, since we are told the wire has resistance. So it's just like your usual DC circuit with heat being dissipated in a resistor caused by charge carrier collisions with the molecules of the resistor.

The energy comes from whatever is causing the varying magnetic field. This causes an induced EMF that induces current, and then energy is lost as heat as described above.

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  • $\begingroup$ Sir my question was something like this -- What form of energy finally converts into heat because the induced electric field does not have a Potential associated with it? $\endgroup$
    – Tony Stark
    Commented Aug 29, 2020 at 13:14
  • $\begingroup$ @TomyStark But it does. That is what an induced EMF is. $\endgroup$
    – BioPhysicist
    Commented Aug 29, 2020 at 13:18
  • $\begingroup$ @Tony Stark it is the energy related with the source or the cause of changing magnetic field. $\endgroup$
    – Ankit
    Commented Aug 29, 2020 at 13:19
  • $\begingroup$ Sir if you don't mind,can you provide a step - step explanation commenting about how energy actually "reaches" from source to heat ,say via magnetic field ,then electric field and then heat? $\endgroup$
    – Tony Stark
    Commented Aug 29, 2020 at 14:55
  • $\begingroup$ @TonyStark I thought I did that at the bottom of my answer. To give more details you would need to give more details first e.g. in where the magnetic field is coming from, etc. $\endgroup$
    – BioPhysicist
    Commented Aug 29, 2020 at 14:59
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Okay let's start with the changing magnetic field. We know that in the region of time varying magnetic field , electric field is induced and ( they have some energy released by the source and it depends on the process involved in bringing the change) and when a coil is placed in this region then the electrons experience a net force as shown in the figure.

enter image description here

Since the force is acting tangentially, the induced electric field does a net work on those charges and hence the energy of the electric field is transferred to those electrons . Since there is an attractive force between the atoms of the coil and the moving electrons ( i.e. resistance of coil ) , energy is released out by the electrons in the form of heat.

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  • $\begingroup$ @Tony Stark was my answer helpful ? Or do you have any doubts regarding my answer ?? $\endgroup$
    – Ankit
    Commented Aug 29, 2020 at 15:46
  • $\begingroup$ Your answer is pretty good. But the problem is that is exactly the way I understand it. It does not have the variations I was looking for. But I am sure that it would be helpful to others. $\endgroup$
    – Tony Stark
    Commented Aug 30, 2020 at 2:25
  • $\begingroup$ @Tony Stark why do you think there must be something different happening ? $\endgroup$
    – Ankit
    Commented Aug 30, 2020 at 2:43
  • $\begingroup$ See the comment posted by @Neil_UK . I was looking for that statement clearly stated. $\endgroup$
    – Tony Stark
    Commented Aug 30, 2020 at 2:48