I've learnt an electromagnetic field is produced by moving charges, i.e. a current.

Is it the case, or is it actually the fact that the charge is changing at a given location?

I mean: imagine I have a charge $q_1$ located at a given point of the space. Then imagine the charge changes and becomes $q_2$, but without moving (this is probably impossible? but let's imagine). Does it produce an electromagnetic field?

Or, without "imagining" a charge changes over time:
Is the EM field produced by the movement of the charge, of by the fact the charge vanishes from its location?

  • $\begingroup$ How can charge change without moving? I can't even assume that. $\endgroup$ – Wrichik Basu Jul 3 '17 at 10:50
  • $\begingroup$ I don't know, and I said: "this is probably impossible". It's like these impossible experiences of thought that are almost not verifiable. Also, I don't know, but I thought it could be like the mass that seems to be constant but is actually not. $\endgroup$ – Evariste Jul 3 '17 at 10:56

I have a charge ... located at a given point of the space. Then imagine the charge changes ..., but without moving (this is probably impossible? ... Does it produce an electromagnetic field?

Elementary charges (electron, proton and their anti-particles) in unbounded state have unchangable charges and by this electric fields of certain size.

Charges emit EM radiation in the case of accelerations. This acceleration can be a spiral path induced by a magnetic field or be this during the deflection from an electric field.

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Synchrotron radiation .............................................................Bremsstrahlung

But there is one more detail. During the approach to the nucleus the electron emits EM radiation, called spontaneous emission. The energy for the emission has to come from somewhere. Now your point of a changing electric field come into play.

What if the electric fields of the electron and the proton inside an atom get weaker during the approach of the electron towards the nucleus? The excess energy wil be realized in the form of EM radiation.


Regarding a change in the charge, when you say

this is probably impossible? but let's imagine

─ let's not. Electric charge is conserved, both globally and locally, i.e. it obeys the continuity equation $$ \frac{\partial \rho}{\partial t}+\nabla\cdot\mathbf j=0, $$ and this is absolutely critical for Maxwell's equations to be internally consistent. All changes in the charge distribution can ultimately be traced down to the physical transport of particles moving from one place to another.

If you want to "imagine" a world where the laws of physics are so different that the total charge enclosed inside a given surface can change without there being a corresponding flux of charge through the surface, then you're no longer describing electromagnetism as we know it, and it is completely pointless to speculate about how radiation might look like in such a theory.

  • $\begingroup$ Thanks Emilio. I understand the charge cannot change by itself, and as you say, thus it "nullifies" my question. However, I could not imagine the Maxwell's equations/classic electromagnetic laws could be a definitive proof, as they may suffer "exceptions" like in the case of quantum physics. $\endgroup$ – Evariste Jul 3 '17 at 11:00
  • $\begingroup$ @Evariste Maxwell's equations don't suffer "exceptions" in any known physics, not even in quantum mechanics, and there are deep theoretical reasons for charge conservation to hold (both in QM and classical EM) as well as comprehensive experimental evidence (a.k.a. all of known EM). If you want to discuss "alternative physics", this is not the venue. $\endgroup$ – Emilio Pisanty Jul 3 '17 at 11:13
  • $\begingroup$ I really don't want to discuss "alternative physics". I'd like first to understand the actual one. As per this answer: physics.stackexchange.com/a/169569/86834, I though Maxwell's law did not apply in quantum physics. $\endgroup$ – Evariste Jul 3 '17 at 11:51
  • $\begingroup$ To the extent that Maxwell's law can be formulated in quantum mechanics, it does hold; what changes is the mechanics around it, but the core of electrodynamics (including the conservation of charge) is very much preserved. If anything the conservation of charge (as the conservation law associated with the basic $\rm U(1)$ gauge symmetry) is even more of a central tenet in quantum physics than in classical mechanics. $\endgroup$ – Emilio Pisanty Jul 3 '17 at 12:51

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