# Field outside of a straight wire

• I
Hi,

Can people please help me with this both qualitatively and quantitatively...

1) If I have a long straight wire carrying a DC current, what field(s) should I expect outside of it?

2)a) If, as an example, I had a stream of charge particles (say electrons), moving perpendicular across the long straight dc current carrying wire what would happen to them?
b) For the quantitative aspect, if these was an electron, traveling at a non relativistic speed of say 1e7 m/s, what force would be exerted on it by a dc current carrying wire having a current of say 5A?
c) If we were to measure the deflection of this electron at some distance further along its path, say we had a phosphor screen some 10 cm away, how much would the electron be deflected by (relative to a zero deflection with the current source turned off)? Would this deflection be in one plane or two (i.e., vertical or horizontal... and/or would there also be an axial change in velcity (i.e., in z)?

This is a seemingly simple case yet I am struggling to understand it.

any help or suggestions would be appreciated.

thanks!

## Answers and Replies

1) If I have a long straight wire carrying a DC current, what field(s) should I expect outside of it?

2)a) If, as an example, I had a stream of charge particles (say electrons), moving perpendicular across the long straight dc current carrying wire what would happen to them?
b) For the quantitative aspect, if these was an electron, traveling at a non relativistic speed of say 1e7 m/s, what force would be exerted on it by a dc current carrying wire having a current of say 5A?
c) If we were to measure the deflection of this electron at some distance further along its path, say we had a phosphor screen some 10 cm away, how much would the electron be deflected by (relative to a zero deflection with the current source turned off)? Would this deflection be in one plane or two (i.e., vertical or horizontal... and/or would there also be an axial change in velcity (i.e., in z)?

This is a seemingly simple case yet I am struggling to understand it.

any help or suggestions would be appreciated.

perhaps you are aware that current carrying conductors involve magnetic field around it and electric field at some distance say R.
so please make a calculation for B as well as E say at R and
then one has to look up the effect on the moving charge.... using the charge times E as force due to electric field and vXB due to the magnetic field- so the charged particle will be under the action of these two force-field...the final path can be interesting

• strokebow
perhaps you are aware that current carrying conductors involve magnetic field around it and electric field at some distance say R.
so please make a calculation for B as well as E say at R and
then one has to look up the effect on the moving charge.... using the charge times E as force due to electric field and vXB due to the magnetic field- so the charged particle will be under the action of these two force-field...the final path can be interesting
Thanks!
Good suggestion. So essentially attempt to apply Lorentz force law to this case and I should be able to get an answer. Lets see what it gives...

perhaps you are aware that current carrying conductors involve magnetic field around it and electric field at some distance say R.
so please make a calculation for B as well as E say at R and
then one has to look up the effect on the moving charge.... using the charge times E as force due to electric field and vXB due to the magnetic field- so the charged particle will be under the action of these two force-field...the final path can be interesting
How do you suppose the motion would behave?

jtbell
Mentor
current carrying conductors involve magnetic field around it and electric field
Current-carrying conductors are usually considered to be electrically neutral as a whole (equal numbers of protons and electrons, with some of the electrons moving to form the current), and therefore produce no electric field.

• strokebow
Current-carrying conductors are usually considered to be electrically neutral as a whole (equal numbers of protons and electrons, with some of the electrons moving to form the current), and therefore produce no electric field.

your argument is 'usually' taken to be true but i have seen somewhere a reference to electric field around a current carrying wire-

<Outside a current carrying conductor, there is, in fact, an electric field. This is discussed for example, in "Surface charges on circuit wires and resistors play three roles" by J. D. Jackson, in American Journal of Physics -- July 1996 -- Volume 64, Issue 7, pp. 855 . To quote Norris W. Preyer quoting Jackson, "Jackson describes the three roles of surface charges in circuits: "(1) to maintain the potential around the circuit, (2) to provide the electric field in the space around the circuit, (3) and to assure the confined flow of current."">

• cnh1995, strokebow and Delta2
Delta2
Homework Helper
Gold Member
There is an electric field even outside a DC current carrying conductor because of the well known surface charges, however the surface charges contributions tend to cancel out in far (big distances in comparison with say the diameter of the wire) distances because the conductor is neutral as a whole.

• strokebow
Khashishi
Science Advisor
Look up and apply the Biot-Savart law and the Lorentz force law.

Current-carrying conductors are usually considered to be electrically neutral as a whole (equal numbers of protons and electrons, with some of the electrons moving to form the current), and therefore produce no electric field.

your argument is 'usually' taken to be true but i have seen somewhere a reference to electric field around a current carrying wire-

<Outside a current carrying conductor, there is, in fact, an electric field. This is discussed for example, in "Surface charges on circuit wires and resistors play three roles" by J. D. Jackson, in American Journal of Physics -- July 1996 -- Volume 64, Issue 7, pp. 855 . To quote Norris W. Preyer quoting Jackson, "Jackson describes the three roles of surface charges in circuits: "(1) to maintain the potential around the circuit, (2) to provide the electric field in the space around the circuit, (3) and to assure the confined flow of current."">

There is an electric field even outside a DC current carrying conductor because of the well known surface charges, however the surface charges contributions tend to cancel out in far (big distances in comparison with say the diameter of the wire) distances because the conductor is neutral as a whole.
Thanks for responses. Very interesting.

I'm a little confused by these responses though. It there a consensus here?

Does an electric field exist outside a DC current carrying wire as I originally described?

If yes, how significant is it? Would it be deemed negligible for the case I described originally. Would it have any significant effect on an electron passing over over it? What parameters would determine the strength of that field (e.g., CSA of wire?, Current through the wire?)?

jtbell
Mentor
Does an electric field exist outside a DC current carrying wire as I originally described?

It seems it really exists, contrary to my original statement. Here are a couple of previous threads on this topic:

https://www.physicsforums.com/threads/electric-field-due-to-current-carrying-wire.709254/
https://www.physicsforums.com/threa...nd-a-current-carrying-conductor.775739/page-2

Towards the end of the second thread is a link to a paper with equations for the electric field outside a straight current-carrying wire with length L, subject to an assumption about the configuration of the rest of the circuit.

This was an interesting surprise for me. I don't think it's usually discussed in introductory and intermediate-level E&M courses. At least Griffiths's intermediate-level book doesn't mention it. I don't remember if Jackson's graduate-level book does, and I don't have a copy any more, to check.

• drvrm and strokebow
It seems it really exists, contrary to my original statement.

Towards the end of the second thread is a link to a paper with equations for the electric field outside a straight current-carrying wire with length L, subject to an assumption about the configuration of the rest of the circuit.

This was an interesting surprise for me. I don't think it's usually discussed in introductory and intermediate-level E&M courses. At least Griffiths's intermediate-level book doesn't mention it. I don't remember if Jackson's graduate-level book does, and I don't have a copy any more, to check.

Thanks for replying. Interesting threads.
A couple of queries:

1) Ive had a read through and am not sure what the assumption is? What is it, and is it reasonable?
2) Do you know of any other text books that mention this? Is this a relatively new 'discovery'? Or is it not quite fully understood. What is the general state of knowledge/consensus on this seemingly very simple yet crucially fundamental case in question?

jtbell
Mentor
1) Ive had a read through and am not sure what the assumption is? What is it, and is it reasonable?
Finite current-carrying wires do not exist in isolation; you need a complete circuit. In order to calculate the fields from a straight wire you need to assume a configuration for the rest of the circuit. That is, how does the current return from one end of the wire to the other? The paper has a diagram showing the circuit that the author analyzed.
2) Do you know of any other text books that mention this?
No, but I'm really familiar only with Griffiths, and a few lower-level books like Halliday & Resnick. It's been a long time since I've used or seen Jackson's book. Maybe someone else has seen a book that covers this topic.

• strokebow
Finite current-carrying wires do not exist in isolation; you need a complete circuit. In order to calculate the fields from a straight wire you need to assume a configuration for the rest of the circuit. That is, how does the current return from one end of the wire to the other? The paper has a diagram showing the circuit that the author analyzed.

Thanks. That very interesting. So are you saying that in any practical case, that is to say a complete circuit, then there will be no electric field generated?