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In all the examples of generation or existence of Magnetic Field energy I have seen so far, I couldn't find any example, where magnetic field energy is created without Non Conservative Electric field, which in turn is generated by Time Varying Magnetic Fields. So, would it be right to generalize that the only source of Magnetic Field energy is, Non Conservative Electric Field?

I am aware that current carrying wire generates magnetic field around it, but I believe that is also caused by the Non Conservative Electric Field, which came into existence into the circuit, when current was building into it, due to the Self Inductance of the wire. Initially when the current was building, the current was variable and so the magnetic field around it was variable, which gave rise to non conservative electric field, which extracted some energy from the source and stored it in the magnetic field around the current carrying wire.

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No.

Any static electric current will generate a magnetic field which is not attributable to a non-conservative electric field. I'm unsure why you haven't been exposed to that example, but you can find it in the introductory section of the magnetism chapter of pretty much every textbook on electromagnetism.

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  • $\begingroup$ Thanks for your response. I am aware that current carrying wire generates magnetic field around it, but I believe that is also caused by the Non Conservative Electric Field, which came into existence into the circuit, when current was building into it, due to the Self Inductance of the wire. Initially when the current was building, the current was variable and so the magnetic field around it was variable, which gave rise to non conservative electric field, which extracted some energy from the source and stored it in the magnetic field around the current carrying wire. $\endgroup$
    – Devansh Mittal
    Commented Aug 31, 2018 at 18:42
  • $\begingroup$ Bold face is appropriate here! $\endgroup$
    – garyp
    Commented Aug 31, 2018 at 18:45
  • $\begingroup$ @DevanshMittal That is incorrect - it is perfectly possible to set up an electric current using a conservative electric field, and the only way that the transients generated at start-up can be interpreted as "creating" the field is if you have a personal sui generis re-definition of that term. But if you've already decided what you will or won't believe, there's absolutely no point in discussing it. $\endgroup$
    – Emilio Pisanty
    Commented Aug 31, 2018 at 18:59
  • $\begingroup$ @Emilio Pisanty - Thanks for your response. I am definitely open to learn and revise my understanding. Kindly help me further. If I understand right, a steady current is not achieved instantaneously. It will take some time to reach, and during that time, the current is variable, so thus the magnetic field, which will result into the production of Non Conservative Electric Field. Isn't it true? If Yes, then can't we say that the creation of magnetic field energy around a current carrying wire is MEDIATED by the Non Conservative Electric Field? $\endgroup$
    – Devansh Mittal
    Commented Aug 31, 2018 at 19:03
  • $\begingroup$ That is technically correct, but it is perfectly possible to do an adiabatic ramp-up of the current, where you turn the current on slowly, which makes that component negligible. For any (continuous) measure of the non-conservative component of the electric field that you care to name, it can be made arbitrarily small by making the ramp sufficiently long. $\endgroup$
    – Emilio Pisanty
    Commented Aug 31, 2018 at 19:11
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Magnetic field is produced by moving charges. So, whatever energy source can move charges, could be a source of the magnetic field energy associated with the moving charges.

Besides the time varying magnetic field, charges could be moved by static electric field, heat (thermionic emission), light (photoelectric effect) or mechanical action (vibrating a charged glass rod).

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  • $\begingroup$ I agree with you. I also believe Magnetic Field Energy creation must be MEDIATED by the Non Conservative Electric Field, in all the cases you mentioned and that is what I intend to ask in this question. Kindly comment. $\endgroup$
    – Devansh Mittal
    Commented Aug 31, 2018 at 18:49
  • $\begingroup$ @DevanshMittal Could you point to a reference to back up that statement? $\endgroup$
    – V.F.
    Commented Aug 31, 2018 at 19:09
  • $\begingroup$ I do not have any reference to back that statement, but in all the examples I notice magnetic field energy, in all such cases, somewhere during its creation, the time varying magnetic field must have come into existence, which gives rise to Non Conservative Electric field. Don't you think so? This is why I say, magnetic field energy is mediated by non conservative electric field. Could you point to any counter example? Kindly also read my comments to Emilio. $\endgroup$
    – Devansh Mittal
    Commented Aug 31, 2018 at 19:19
  • $\begingroup$ My understanding primarily follows from the example of an Inductor. In an inductor, the work done by the Non Conservative Electric Field, turns out to be equal to the energy stored in the Magnetic Field Energy. It is true that this energy comes from the source (battery for example), but the conversion of energy is mediated by Non Conservative Electric Field. Isn't it? $\endgroup$
    – Devansh Mittal
    Commented Aug 31, 2018 at 19:33
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    $\begingroup$ @DevanshMittal When the current and its magnetic field is increasing, a non-conservative electric field is created, but, in this case, it is the effect - not the cause - of the changing magnetic field. I am far from claiming that this exhaustively describes what is going on, but I would not speculate what else might be happening that could potentially invalidate this logic. $\endgroup$
    – V.F.
    Commented Aug 31, 2018 at 20:42
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would it be right to generalize that the only source of Magnetic Field energy is, Non Conservative Electric Field?

Not in physicist's English, because that's not how "source" of energy is thought and spoken of.

"Source of energy" refers to a body or a region of space that already contains energy, part of which then moves into another body or a region of space which we study and which is the object X in statements like "energy of/in X increases/decreases".

What you're observing is that change of magnetic energy in a fixed region of space is necessarily associated with change of magnetic field strength somewhere in there, and thus, due to Maxwell's equation, to a curl of electric field there being non-zero. This does not mean that only non-conservative part of electric field is source of energy (because field is not a body or a region of space), but it also does not mean that only non-conservative field is responsible (doing the work) for the energy transformation from electric to magnetic form. It just means that whenever there is change of magnetic energy density, total electric field is non-conservative.

Of course, when electric field in a wire has both conservative and non-conservative component, it is the total electric field that does the work on the current, thus both conservative and non-conservative component participate in the energy transformation.

When you check directions and signs in inductor where current increases in time, the induced electric field of the inductor (the major part of non-conservative part of the total electric field) in the winding actually opposes the increasing current, thus some other force is responsible for the current increase and also for magnetic energy increase. This is usually (in lumped circuits) electrostatic force due to a capacitor or a battery or other voltage source, to which the inductor is connected. So more correct thing would be to say that the source of the magnetic energy is the electric energy in the capacitor or chemical energy in the battery, and when inductor's magnetic energy increases, it is the conservative electric force that does work against the induced electric force, and most of this work (assuming negligible losses) would transform into magnetic energy. In practice losses aren't negligible, so some part of the work transforms into internal energy of the winding (manifesting via increased temperature).

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  • $\begingroup$ Wow. Wonderful response. As always, you understand the spirit of my questions exactly and respond accordingly. In the past also you have responded to my questions amazingly. Thanks a lot for all your responses. $\endgroup$
    – Devansh Mittal
    Commented Jan 23 at 15:26
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The formation of magnetic field due to non-conservative electric field is not the only way.If you have studied the hysteresis loop in detail then you easily see that by increasing the external electric field around a ferromagnetic substance the polarisation occurs in such a way that it hits a saturation point from where a magnetic field gets in existence and that to from a conservative electric field. For more details check out :- https://youtu.be/sEGLcpmIIBY?si=DT7lvWzVzpSK6qPs

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Magnetic energy is not created by an electric field, but by moving charge. The charge. This motion can be caused by any force, including an electric one.

The rotation of an electric field is the same thing as the time derivative of a magnetic field. It does not generate it.

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  • $\begingroup$ It is not the same concept thing, but according to laws of electromagnetism, these two quantities are always proportional to each other. $\endgroup$
    – Ján Lalinský
    Commented Jan 21 at 22:30