Batteries and the electric field inside a wire

[Janez]

I have a question what does create a electric filed inside coducting wire? And is it the same field trought the whole wire? Thanx for answers.

 

[oz93666]

I have a question what does create a electric filed inside coducting wire?

Your terminology is not quiet correct ... the electric field is across the two ends of the wire , if it is connected to a battery for example . This electric field (more correctly 'electric potential' ) , created by the battery is from a chemically created excess of electrons at one end.

And is it the same field trought the whole wire? Thanx for answers.

The potential will change uniformly down the length of the wire , if the wire has uniform resistance.

 

[Janez]

No I meant electric field. I know there is potencial diffrence between ends, but ther is also electric field insede wire. And electric fieled is a field so it is evrywhere, just sometimes its value might be zero.

 

[oz93666]

No I meant electric field. I know there is potencial diffrence between ends, but ther is also electric field insede wire. And electric fieled is a field so it is evrywhere, just sometimes its value might be zero.

Well ... it's only the potential which creates the field ...

Imagine the +and - above are terminals of a battery ... once you put a wire across , this channels the "field".

 

[Janez]

Ok, than the question is how wire chanes the field?

 

[Delta2]

In the beginning there is only the potential difference of the battery and the relevant charge densities at the poles of the battery. After that the charge densities start flow into the good conducting wires (because of the initial Electric Field that exists there when we bring a piece of wire close to one pole of the battery). This flow of charges is essentially a current, and this current travels down to the wires as a wave according to the laws of Maxwell's equations and Ohm's Law (for more on that you might want to read on transmission line theory https://en.wikipedia.org/wiki/Transmission_line) and this current wave has the speed of light. This current flow is essentially responsible for all the surface charge densities that will appear in all parts of the circuit, even those parts that are distant to the poles of the battery. These surface charge densities are responsible for the E-field along the wires.

Something to think on: The total charge of the circuit is zero or almost close to zero. It is just that the battery with the current flowing mechanism has established a charge separation though out the circuit using not only the charges that were initially on the poles of the battery but those that were as free electrons in the conducting wires as well. That is we have a circuit where some parts are charged positive and some other parts are charged negative, yet the total charge is zero.

 

[Meir Achuz]

"And is it the same field throughout the whole wire?"
The current in a wire is I=V/R. The electric field at any point in the wire is E=I\sigma/A, where \sigma is the conductivity, and A is the cross-section area of the wire. If A is constant, E is constant. If A varies, E~1/A.

 

[Janez]

Ok so what is than the source of electric field in conducting wire? Not the voltage of battery but the electrons in the wire?

 

[Meir Achuz]

The source of the electric field is the voltage in the battery. The magnitude of E at any point in the wire is given by my first answer.

 

[Delta2]

I think its more accurate to say that the EMF of the battery is indirectly responsible for all the electric field in the circuit. However and since from Jefimenko's equations (https://en.wikipedia.org/wiki/Jefimenko's_equations) the sources of electric field can be either
1) charge density $\rho$
2) time varying current density $J$
and since 2) is excluded since we have a DC battery in the circuit,
we can say that the "more direct " or "more immediate" sources of the electric field in the wire are the surface charge densities in the surface of the wire and the poles of the battery.

 

[rude man]

"And is it the same field throughout the whole wire?"
The current in a wire is I=V/R. The electric field at any point in the wire is E=I\sigma/A, where \sigma is the conductivity, and A is the cross-section area of the wire. If A is constant, E is constant. If A varies, E~1/A.

The formula is I/A = σE. If σ=∞ (perfectly conducting wire) then E will be zero. If the wire has resistance then the formula is IR = d(Es + Em) where d is the length of the wire of resistance R.

Em is the emf-induced field such as that produced by a battery, or magnetically induced, or other process resulting from the conversion of energy into electrical energy. Es is the static E field such as that across a resistor in a battery circuit and begins and ends on charges. A battery comprises opposing Em and Es fields, resulting in net zero E field in the battery. A wire of finite resistance can hold either Em, Es or both.

The total E field is just Em + Es, algebraically summed.

 

[Delta2]

@rude man can we say that the field you call $E_m$ is the electric field component due to the vector potential and the $E_s$ is the electric field component due to the scalar potential?

 

[rude man]

@rude man can we say that the field you call $E_m$ is the electric field component due to the vector potential and the $E_s$ is the electric field component due to the scalar potential?

Hello @Delta2,
The latter statement is definitely correct. The scalar potential, which I and most people just call the potential or voltage, is the line integral of Es.

I'm not sure about a connection between Em and the vector potential. Frankly, I have never dealt with an electric field vector potential (just a magnetic one). But I don't see it myself: if a vector potential V exists, then E = ∇xV only if ∇⋅E = 0 (just math) but of course Maxwell says ∇⋅E = ρ/ε. So if there is no charge then OK, but maybe we can just forget about it.

However, you might check the papers of Princeton professor K.T. McDonald which I cited in a footnote my Insight article. He emphasizes calling the conventional potential the "scalar potential" and may have mentioned a vector potential as well.

 

[Delta2]

By vector potential I mean the magnetic potential $\vec{A}$ (which is a vector with 3 components) such that $\vec{B}=\nabla\times \vec{A}$ and $\vec{E}=-\nabla V-\frac{\partial \vec{A}}{\partial t}$

So $E_s=-\nabla V$ and $E_m=-\frac{\partial \vec{A}}{\partial t}$ that's what I meant.

 

[rude man]

By vector potential I mean the magnetic potential $\vec{A}$ (which is a vector with 3 components) such that $\vec{B}=\nabla\times \vec{A}$ and $\vec{E}=-\nabla V-\frac{\partial \vec{A}}{\partial t}$

So $E_s=-\nabla V$ and $E_m=-\frac{\partial \vec{A}}{\partial t}$ that's what I meant.

Em is not a magnetic field component, it's an electric one.

As example, the E field in a propagating e-m wave is an Em electric field since ∇xE = -dB/dt ≠ 0. In that case, the E field must be purely Em since ∇xE = 0 if E is purely Es.

Another example, if you have a uniform-resistance ring surrounding a time-varying B field then emf = -dφ/dt = 2πa Em = ir where a is the radius of the ring, i the current and r the ring resistance. Es = 0 everywhere and there is no potential. On the other hand, if the ring resistance were non-uniform with resistance r in one half and 2r in the other half, then both Em and Es fields would be present in the ring.

The distinction between Es and Em is significant as I have tried to explain in my Insight blog.

EDIT: I don't think I answered your question. Please see my next post when it's ready
@rude man

 

[rude man]

@Delta2,
if the emf is generated magnetically then I think the answer is yes: E = Em = -∂A/∂t. This is because the E field in the dynamic version includes the static component Es = -∇V but if there is no Es then there is no -∇V. So all that's left is -∂A/∂t and must be Em.

However, emf can be generated other than magnetically. For example, as I discussed in my blog, a battery also generates emf so there must exist an Em field within the battery. Which it does. So in that case Em is not included in -∂A/∂t if A is defined by B = ∇xA.

 

[Joseph M. Zias]

There has been a plethora of articles in recent years on this topic, including the fact that power flow is actually on the outside of the wire, via the Poynting vector. Surface charge locations associated with the guidance of the electric field inside and outside the wire have been a topic of discussion. Here is a bibliography of some articles on those subjects: For an easy read look at the web page for amasci below.

W.G.V. Rosser. “What makes an electric current flow“, Am. J. Phys. 31 , 884-885 (1963)

Ian Michael Sefton, “Understanding Electricity and Circuits What the Texts Books Don’t Tell You”, Science Teachers Workshop, 2002, Sydney, Australia

J. D. Kraus, Electromagnetics, 2nded. (McGraw-Hill, 1973) p 416-418

J. D. Kraus, Electromagnetics, 4thed. (McGraw-Hill, 1992) p 577-580

W. Beaty, “In a simple circuit, where does the energy flow?”, Science Hobbyist,
http://amasci.com/elect/poynt/poynt.html(12, 2000)

R. W. Chabay and B. A. Sherwood, Matter & Interactions, 4th ed. (Wiley
New York, 2015).

R. W. Chabay and B. A. Sherwood, “A unified treatment of eletrostatics
and circuits” (2006).

3J. D. Jackson, “Surface charges on circuit wires and resistors play three
roles,”Am. J. Phys. 64, 855–870 (1996).

M. A. Heald, “Electric fields and charges in elementary circuits,” Am. J.
Phys.52, 522–526 (1984).

N. W. Preyer, “Surface charges and fields of simple circuits,” Am. J. Phys.
68, 1002–1006 (2000).

I. Galili and E. Goihbarg, “Energy transfer in electrical circuits: A qualitative
account,”Am. J. Phys. 73, 141–144 (2005).

M. K. Harbola, “Energy flow from a battery to other circuit elements: Role
of surface charges,” Am. J. Phys. 78, 1203–1206 (2010).

A.K.T. Assis and J.A. Hernandes, The Electric Force of a Current, (C. Roy Keys, Inc. Montreal, Quebec) 2007 (ISBN: 978-0-9732911-5-5)

Rainer Muller, “A semiquantitative treatment of surface charges in DC circuits” Am. J. Phys. 80,
(9), Sept. 2012.

 

[rude man]

The amasci paper is very good.

Might have included what goes on inside the wires as well: inside the wire the E field is entirely parallel to the flow of current (the charges are on the wire surface so the larger external E field is mostly normal to it).

If the wire resistance is not zero there is a small component of the P vector normal to the wire surface; it enters the wire and is dissipated by the time it reaches the center of the wire axis. There is also a small E component tangential to the wire equal to the E field within the wire.

The main point remains the fact that most of the power flow is tangential to the wire and thus to the E field inside the conductor, and the current. That's what a wire is usually for: to guide power along it.

EDIT: after reading the pertinent secion of Feynma's Chapt. 27 I think amasci has misrepresented what Feynman says. I quote: "You don’t need to feel that you will be in great trouble if you forget once in a while that the energy in a wire is flowing into the wire from the outside, rather than along the wire. It seems to be only rarely of value, when using the idea of energy conservation, to notice in detail what path the energy is taking." And "It is not a vital detail, but it is clear that our ordinary intuitions are quite wrong."

In other words, Feynman clearly states that the idea of energy propagating with the current is wrong, but that "forgetting" it does not usually lead to energy conservation errors.

 

[Joseph M. Zias]

The amasci paper is very good.

Might have included what goes on inside the wires as well: inside the wire the E field is entirely parallel to the flow of current (the charges are on the wire surface so the larger external E field is mostly normal to it).

If the wire resistance is not zero there is a small component of the P vector normal to the wire surface; it enters the wire and is dissipated by the time it reaches the center of the wire axis. There is also a small E component tangential to the wire equal to the E field within the wire.

The main point remains the fact that most of the power flow is tangential to the wire and thus to the E field inside the conductor, and the current. That's what a wire is usually for: to guide power along it.

EDIT: after reading the pertinent secion of Feynma's Chapt. 27 I think amasci has misrepresented what Feynman says. I quote: "You don’t need to feel that you will be in great trouble if you forget once in a while that the energy in a wire is flowing into the wire from the outside, rather than along the wire. It seems to be only rarely of value, when using the idea of energy conservation, to notice in detail what path the energy is taking." And "It is not a vital detail, but it is clear that our ordinary intuitions are quite wrong."

In other words, Feynman clearly states that the idea of energy propagating with the current is wrong, but that "forgetting" it does not usually lead to energy conservation errors.

I suggest looking at some of the other items in the bibliography, I thought Krauss gave a good account and he was an E&M expert. Some of the others are intense in their treatment of the subject with vectors and so on. I thought it interesting that one of the earliest articles was from 1963.