# Why do electrons accumulate on the surface of a wire (along its length) when a voltage source is applied across the wire cross section?

When I was going through how electric fields are transmitted long distances through a wire, I read that there was accumulation of charges along the surface of the conductor to drive the fields to long distances.

Why do the charges accumulate on the surface of the wire although the field is parallel to that surface? Why can't it be just volume charge driving the field in the wire?

• This might be relevant : physics.stackexchange.com/q/328971/207455 – user207455 Jun 17 at 13:13
• @Solar Mike Actually I do understand that when electric field is perpendicular to the surface the electric charges accumulate there but in wire they are accumulating along the surface where electric field is parallel – Trilok Girish Kamagond Jun 17 at 14:06
• Look at this paper and associated simulations. It is a very rich simulation, and takes some time to grok. Note that there is a drop down menu; to see where things are going, you might want to take a quick look at the "simple circuit" option. Note also that the simulation can visualize the fields due to the EMF source, and the fields due to surface charges. The article and simulation provide a fairly complete answer. – garyp Jun 17 at 18:46
• @garyp thank so much for the resources, I will go through them. – Trilok Girish Kamagond Jun 17 at 19:06

Why will the charges accumulate on surface of the wire although the field is parallel to that surface? Why can't it be just volume charge driving the field in wire?

Regardless of the direction of the electric field with respect to the direction of the conductor, electrical charge will accumulate on the surfaces of the conductor if they have nowhere else to go. This is the case if a conductor is isolated in space. If the conductor is part of a circuit with a source of EMF it need not accumulate. Refer to the diagrams below.

The first diagram below shows a section of an isolated conductor that is not in an electric field (top diagram), and the same section of isolated conductor placed in an electric field perpendicular to the conductor. By convention the direction of the electric field is the direction of the force that a positive charge would experience if placed in the field. Note that electrons move to the left surface of the conductor, being attracted by the field, leaving the right surface positively charged, as the charge has nowhere to go. The electric field produced in the conductor due to the movement of charge is equal and opposite to the external applied electric field so that the net field inside the conductor is zero.

The bottom diagram shows a conductor connected to a battery to form a complete circuit. The battery produces an electric field inside and parallel to the conductor. Electrical charge is therefore free to move in the conductor from one battery terminal to the other, instead of accumulating. By convention, current is the flow of positive charge. So positive charge will flow from the positive terminal of the battery to the negative terminal. This is the same as electrons flowing from the negative terminal to the positive terminal. All conductors (except super conductors) have resistance, so the total drop in electrical potential of the charge as it moves through in the conductor due to its resistance equals the increase in potential provided by the battery.

Bottom line: The difference between the top diagram and bottom diagram is in the top diagram the electrical conductor is isolated in space and the charge has no where to go but accumulate to relieve the force due to the external field, whereas in the bottom diagram the conductor is not isolated in space but connected to a source of EMF that takes charge from one end of the conductor and moves the charge to the other end of the conductor.

Hope this helps.

• the link here tells that there is accumulation of charges physics.stackexchange.com/questions/5277/… – Trilok Girish Kamagond Jun 17 at 15:37
• I think that the OP has asked a question different from the one you answered. – garyp Jun 17 at 18:38
• @garyp Yes, I realized that after the OP commented on my answer. Working on a revision. Thanks. – Bob D Jun 17 at 18:39
• @garyp The thing is, I'm not sure that charges actually accumulate on the surface in my second diagram, although I admit seeing it illustrated that way several times. I'm more inclined to believe that the charge shown on the surface actually represents the net charge as you move along the conductor, that is, represent the gradient that exists. But to be honest, I'm not sure. – Bob D Jun 17 at 18:42
• Take a look at the comment I posted to the OP. – garyp Jun 17 at 18:47

In what context did you read this? But one explanation might be the following. As you have a steady flow of electrons, through a long wire there might be impurities at the surface of the conductor wire. As a result, electrons will be trapped at the impurities on the surface. Over time this might lead to an accumulation of electrons at the surface.

Why do these impurities have a higher probability to be occupied w.r.t. impurities in the bulk of the wire? Well because of the fact that the scattering of electrons with the impurities in the bulk will be much larger, you will have scattering in all three dimensions, whereas at the surface this is not the case. As a result, the electrons won't remain at the impurity in the bulk, in contrast to impurities at the surface.

• Thank you for your response. Here is the link I reffered physics.stackexchange.com/questions/5277/… in the accepted answer it was mentioned that charges accumulate on surface. – Trilok Girish Kamagond Jun 17 at 14:58
• @TrilokGirishKamagond Yes but it is my understanding that that accumulation only serves to confine the electric field within the conductor. I was trying to differentiate the situation where there is only charge accumulation and no flow of charge vs where there is current flow. I can attempt to revise my diagrams and answer to clarify that. Thanks for pointing it out. – Bob D Jun 17 at 15:46
• @Bob D Actually can you also mention why that accumulation of charges only at surface serves the purpose of confining electric fields inside the conductor. Won't charges arranged in some other fashion serve the purpose. – Trilok Girish Kamagond Jun 17 at 15:49