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TLDR
When switching on an electrical device (e.g. a light bulb or a heater), there is an initial wave (pulse) travelling with very high speed (close to the speed of light) and “carrying the information” that the device was turned on. What is the type of the wave: 1) an EM wave travelling in the free space along the circuit or 2) a matter (“sound”) wave of electrons in “electron gas” inside conductors? Or both types of waves (matter and field waves). What is the mechanism of the wave reflection before the equilibrium current is set (value set by Ohm’s law)?


Full question
Suppose, there are
1) a DC power source,
2) a switch,
3) a resistor,
4) two wires of relatively low resistance (in comparison with the resistor) connecting the source and the resistor.

Before closing the switch there will be charge build-ups at the ends of the switch. When the two ends of the switch are close enough, there will be an arc discharge (switching the circuit on) followed by physical contact of switch terminals (electrical contact). Let's call it the Moment 1 Switching on.

enter image description here

During the discharge there will be accelerated flow of the electrons causing an EM pulse propagating mostly along the wires; likely in both directions (not 100% sure), that is, one to the battery and another to the resistor.

Thereafter, these two pulses will be reflected numerous times at the power source and at the resistor until
1) the energy of the pulses is converted into thermal energy of resistor and wires and
2) the equilibrium is set (Moment 2 Equilibrium).

enter image description here

As for the equilibrium, the the stationary EM field and energy flow is clear (see the picture above) ({1},{2}, {3}). There are static electric and magnetic fields with the Poynting vector $\vec S = \vec E \times \vec B$ lines going from the power source to the resistor and showing the direction of the energy transfer from the source to the resistor (consumer of energy).

The four questions are about physics of transition from Moment 1 Switching on to Moment 2 Equilibrium:


1) How many times initial pulse is reflected back and forth before the equilibrium is reached?
Obviously the answer depends on how ones fixes the Moment 2 Equilibrium:say, the current inside the wire is 90% of equilibrium value ($90\% \cdot {V \over R}$).


2) What physical processes lie behind this “reflection” (describe the mechanism of “reflection”)?


3) Inside what medium (free space or wires) does the pulse propagate? Its trajectory.

I am nearly sure (but not 100%) that propagation of the pulse is happening in the free space surrounding circuit elements, not inside wires, resistor or power source. Please, confirm or disprove.


4) What happens inside the circuit after switching on?
Namely: Are there are any “electronic” (matter) or EM (field) waves inside the conductor carrying the energy or “information” that the circuit was switched on?
The question is about the transient processes between Moments 1 and 2.
If yes, what is the propagation speed of these waves? Is it a wave inside an “electron gas” similar to a sound wave? If yes, what are physical processes behind the transfer of energy inside such an electron “gas”?
Or if it is a propagation of EM waves inside the conductor, what is the propagation speed? Should such a wave be immediately absorbed in the conductors (given abundance of free electrons inside)?

Keep in mind, the phase velocity of light inside copper is on the order of several hundreds meters per second.


PS: Since there are a lot of questions, partial answers are welcome.
PPS: This is a not well-designed circuit. So reflections do occur.

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closed as too broad by sammy gerbil, Gert, ACuriousMind, heather, Rob Jeffries Aug 2 '16 at 22:23

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ There is a similar question , however, it is about the equilibrium state, not the transient one. $\endgroup$ – Sergei Gorbikov Jul 27 '16 at 22:14
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    $\begingroup$ That's a lot of questions... but what happens in detail can only be answered with a full Maxwell simulation as it depends entirely on the geometry. In general a well designed electronic circuit in which this matters will not contain such an open geometry but it will use transmission line structures with well defined impedances, in which case there are no reflections, at all. $\endgroup$ – CuriousOne Jul 27 '16 at 22:22
  • $\begingroup$ @CuriousOne 10x. I updated the question. $\endgroup$ – Sergei Gorbikov Jul 28 '16 at 5:13
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    $\begingroup$ To address your first question, note that a matter wave of electrons would necessarily induce E&M waves, so they are not so distinct. I'm then tempted to say that really both occur and are directly related to each other. If you do circuit QED, however, people usually talk about these things as just photons, or E&M waves. $\endgroup$ – aquirdturtle Jul 28 '16 at 14:20
  • $\begingroup$ @aquirdturtle 10x for the excellent comment. I have a similar feeling, that matter and EM waves are bound together. At least by Maxwell’s equations. No currents, no charges, then no EM field (except plane waves). What I cannot figure out is why the matter (“electrons”) wave travels with speed of light (not speed of “electrons sound”). $\endgroup$ – Sergei Gorbikov Jul 28 '16 at 14:32
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EM waves travels along and in wire (not in free space completely) in circuit. When EM wave travel, it causes electrons in wire to move as well. So , both move simultaneously.

Matter wave does not travel at c.

There is no single matter wave in wire. There are zillions of electron each moving with almost $10^{5}m/s.$ They are always moving.

If you consider drift velocity, it's $~10^{-4} m/s$.

Energy in circuit is carried by EM wave, which is shared with drifting electrons.

So, you don't talk about matter waves in circuit.

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  • $\begingroup$ Thanks for the answer. Several comments: 1) Take 1mmx1mm copper wire, send 1 A of current, put 1 Ohm resistor. Power dissipated will be 1 Wt. The kinetic energy of electrons passing through the cross-section of the wire per unit of time will be on the order of 10^-20 Wt. Therefore, the energy is almost not carried by (shared with) electrons. Cont'd $\endgroup$ – Sergei Gorbikov Jul 31 '16 at 21:15
  • $\begingroup$ 2) Take a nearly ideal conductor, that is, one with very very low resistance, electrical field inside the conductor will be nearly zero (because nearly no potential drop inside it). Thus, the Poynting vector as well is nearly zero in amplitude inside. Thus, the energy transfer happens outside the conductor, not inside it (almost not inside). 3) Fermi speed of electrons in copper is on the order of 10^6, that is about 0.01 c (you mentioned 0.1 c). Please amend if agree. Cont'd $\endgroup$ – Sergei Gorbikov Jul 31 '16 at 21:16
  • $\begingroup$ As for the matter wave, the hypothesis is that after switching on energy may transfer inside electron gas inside a conductor in a similar manner to a sound wave travelling in a solid. Need to be proved or disproved. $\endgroup$ – Sergei Gorbikov Jul 31 '16 at 21:25
  • $\begingroup$ For 3) agreed and amended. $\endgroup$ – Anubhav Goel Aug 3 '16 at 6:24
  • $\begingroup$ Matter waves are deBroglie waves. I think by matter waves , you meant longitudinal sound waves. Okay!! Here you see that , there was no physical impact that would drift electrons from one side to other. Instead it was an electric field in entire wire that drifted electrons. It's like you hammered wire from each cross section. As soon as EMF was applied, electric field reached other end at 0.3c. if wire is of limited length like 1000m, you can say electron from both end drifted together simultaneously. It was nothing like sound wave that would begin from one end and move to other end at 400m/s. $\endgroup$ – Anubhav Goel Aug 3 '16 at 6:38

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