4

I'm reading Sherwood and Chabay's brilliant textbook Matter and Interactions, in particular the section that deals with how the surface charges in an electric circuit distribute themselves to generate the electric field within the wire.

One question left unanswered, however, is why the generated electric field does not affect the surface charges themselves, only the electrons flowing through the wire.

enter image description here

In the above picture, wouldn't the charges on the rings also be affected by each other and the other ring?

1110101001
  • 1,555
  • 1
    The electric field in a wire is not generated by surface charges but by the power source that cause the current flow in the wire. The current density in the wire will then determine the local equipotential surfaces and the surface charges will be in equilibrium with that field. I am not sure what the above drawing is supposed to mean. – CuriousOne Jan 04 '16 at 07:13
  • @CuriousOne If the electric field were generated solely due to the battery, then the field would drop out proportional to the square of the distance. I don't believe this is the case, however. While the battery is the initial source of the field, feedback from this field moves surface charges into positions such that they can propagate this field at steady state. See this document that is essentially an excerpt from the textbook I mentioned. – 1110101001 Jan 05 '16 at 03:08
  • Of course the far field drops with distance... why would't it? The entire setup is not even charged, as a whole, so you don't even get the field of a finite charge but you get the field of a complicated electric multipole, depending on the configuration of the source and the wires. If the book suggests otherwise then it belongs into the garbage. – CuriousOne Jan 05 '16 at 03:19
  • @CuriousOne This related physics.se question seems to suggest otherwise, that during steady state the field remains constant in magnitude throughout the wire, regardless of distance. – 1110101001 Jan 05 '16 at 06:41
  • For a straight wire of constant diameter, yes. I still don't see where the surface charges come in. They simply don't play any role in this problem. You can eliminate all surface charges by coating the wire with a thin insulator and then with an outer conductive surface that will equalize all surface charges. This won't affect the conduction mechanism in the slightest. – CuriousOne Jan 05 '16 at 06:51
  • @CuriousOne Careful when resigning books to the garbage. I suggest you read up on the treatment of surface charges in DC circuits. https://www.tu-braunschweig.de/Medien-DB/ifdn-physik/ajp000782.pdf You'll be surprised at the role they play. The view that the electric field in a DC conductor is generated 'solely by the power source' is insufficiently nuanced and you end up with an indefensible model all too quickly... – DrSAR Nov 07 '16 at 05:51
  • http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/18-SurfaceCharge – 1110101001 Jun 06 '17 at 00:26

2 Answers2

5

It is possible that the surface charges are pinned at sites on the surface, but it is also possible that they are mobile. Even if they are mobile, their contribution to the current is infinitesimal, because I = JA = sigmaEA, and the cross-sectional area associated with the surface charges is completely negligible compared to the rest of the cross-sectional area. So whether the surface charges are mobile or pinned is irrelevant.

You might find it interesting to view this VPython program in your browser (thanks to the new GlowScript version of VPython found at glowscript.org):

http://tinyurl.com/SurfaceCharge

The surface charge distributions were calculated by a charge-field relaxation method described in the "Articles and talks" section of matterandinteractions.org. The VPython programs let you view these distributions and interactively explore the net field everywhere.

Bruce Sherwood, co-author with Ruth Chabay of the Matter & Interactions textbook.

user3786782
  • 176
  • 1
  • 1
    I wasn't explicit about where to find the relaxation method explanation on our web site: Surface Charge Distributions in Circuits, a poster presented by Ruth Chabay and Bruce Sherwood at the winter 2016 conference of the American Association of Physics Teachers in New Orleans. – user3786782 Jan 04 '16 at 03:30
  • 1
    Note too that even if the surface charges are mobile, the surface charge density at any location on the surface in the steady state does not change, so the field contributed by the surface charges doesn't change (definition of the steady state). – user3786782 Jan 04 '16 at 04:22
  • Wow I didn't expect to get an answer from the author himself! I'm still sort of unclear, however, as to why the surface charge density at a given location wouldn't change if the surface charges were moving. Is it because as the charges move further down the wire they would adjust themselves to match the charge density that existed at the time before? – 1110101001 Jan 04 '16 at 04:54
  • The definition of the steady state is that there is current (so not equilibrium) but the current does not change, which means that the field everywhere is constant, which means that the charge density everywhere is constant (does not change with time). Internal to the wire charges move out of a region but the same number of charges move into the region. On the surface, charge may (or may not; I don't know) move away from their present location, but in that time the same amount of charge moves into that location. – user3786782 Jan 04 '16 at 05:03
  • Note that during the transient leading to the steady state the surface charge distribution DOES change with time, and the current DOES change with time. These transient movements of charge eventually lead in the case of a DC circuit to that distribution of charge that, together with the field of the battery, makes a net field everywhere that is consistent with the Kirchhoff loop and node rules. See the poster and program I mentioned. – user3786782 Jan 04 '16 at 05:06
  • @user3786782,I was also very confused ,I am in high school and no on talks how field are generated in the circuit{I know its very complicated to calculate but is it possible to calculate it or its just qualitative?} .at least now I know something, Sir, can u please also explain why capacitor plated should get equal and opposite charges when connected in a circuit, people say as 1 electron accumulate it repels one electron from the other plate but its very vague .why it repels only one electron? its just one case and not general so they shouldn't say that – Arun Bhardwaj Nov 04 '21 at 07:44
  • Here is a later article on calculating the surface charge distribution on a circuit: https://matterandinteractions.org/wp-content/uploads/2019/04/AJP-SurfaceCharge.pdf – user3786782 Nov 05 '21 at 17:51
  • Capacitor: Start with a gap in a resistive wire in a circuit. Between that gap and the positive end of the battery, the surface of the wire will be charged positive, and the other wire will be charged negative. Now insert a capacitor. The plate connected to the positive wire will lose electrons and the plate connected to the negative wire will gain electrons. This rearrangement of charge will stop when the fringe field of the capacitor is equal and opposite to the field in the neighboring wires due to the surface charge on those wires. – user3786782 Nov 05 '21 at 17:54
  • @user3786782 sir, still I think I didn't fully understand this because how do we know fringe field can become equal to fields produced by surface charges and source insiDe the wires they are connected with ONLY when capacitor plates carry equal and opposite charges? The main question is not only applicable to capacitors only I want a reasonable explanation of "KIRCHOFF CURRENT LAW" why the current coming in and out MUST be equal through any electrical component {battery,capacitor,resistor etc} why it CANNOT accumulate anywhere? – Arun Bhardwaj Mar 25 '22 at 17:08
  • @user3786782 say for example , a wire is connected to only negative terminal of a battery we know there will be some surface charge distribution on the wire to cancel the electric field of battery, so it means there will be some positive charge move from the wire to the battery , it means THERE IS some net positive charge accumulated in the battery so the textbooks say battery doesn't accumulate charges? Sir please help me the way electricity is discussed in my textbook is very illogical and often involved several internal assumptions without giving any reason....its very frustrating, ... – Arun Bhardwaj Mar 25 '22 at 17:14
  • @user3786782 Please help me, its about my future ,I wanna know do we have the reasonable explanations to these confusions and assumptions if I study electromagnetism further on college level? or do they still assume steady state already and doesn't talk about things like distribution of surface charge, why transient phase doesn't last long etc? – Arun Bhardwaj Mar 25 '22 at 17:17
  • Sorry, but it's beyond my capability to compensate for the omission from nearly all physics textbooks of any information about how circuits actually work. I do recommend that you study our paper at the matterandinteractions.org URL given above. Or read our textbook; it's a story that in its entirety spreads over three major chapters. – user3786782 Mar 27 '22 at 03:57
  • The "Kirchoff Current Law" should not be used as though it were some very special property of circuits. No, it's really just charge conservation in a steady state. In a steady state, such as in a DC circuit, the amount of charge in any section of the circuit MUST not change (that's the definition of "steady state"), and since charge is a conserved quantity, the same amount of current entering this region MUST be equal to the amount of current leaving this region. Similarly, the "Kirchoff Loop Law" is just another name for the fact that the round-trip path integral of E MUST be zero. – user3786782 Mar 27 '22 at 04:03
  • @user3786782 sir, I saw "veritasium's"video on electricity in which he mentions your book and talk about surface charges role, but the question I still have is- As, we know steady state arises very quickly , so for establishment of surface charges the electrons which piles up at the surface has to come from the surfacial atoms because if they come from inner atoms they need to travel a long distance and that would take much time but if that's how surface charge gradient is actually established then it would.... – Arun Bhardwaj Jan 25 '23 at 11:15
  • @user3786782 create exactly opposite gradient in inner atoms as electrons are leaving from surface leaving behind gradient of positive charges and that would counter the electric field from surface electrons isn't it?so where are the surface charges exactly coming from? Also I have another question from you- textbooks always say that battery always maintains the voltage across its ends via chemical reactions but suppose we have connected just one plate of a capacitor via wire to just positive end of battery.... – Arun Bhardwaj Jan 25 '23 at 11:17
  • @user3786782 we know that there will be some surface charge distribution on the wire and capacitor plate to cancel the electric field of battery so there has to be some excess positive charge on wire and capacitor plate and that can come only from battery so how can battery maintain voltage here? shouldn't it change?chemical reactions aren't some magic which can maintain the voltage all time, I think battery can maintain voltage only after the steady state because in that state the current entering and leaving battery would be same? – Arun Bhardwaj Jan 25 '23 at 11:18
0

The number of electrons on the surface is EXTREMELY small compared to the number of electrons in the wire. Think of it this way: In a metal there is a "sea" of electrons that are not bound to atoms but are free to roam. If this sea expands by an infinitesimal amount, there will be a small (but essential) number of electrons on the surface, and the interior of the wire will remain very nearly neutral. The electrons that move to the surface do NOT travel a long distance to get there; there were already LOTS of free electrons right next to the surface. Sorry, but I don't understand your second set of questions. I strongly recommend that you study the paper whose link is given above.

user356727
  • 1