What does the E field look like in a real circuit?

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Discussion Overview

The discussion revolves around the characteristics of the electric field (E field) in real circuits, particularly focusing on the differences between idealized circuits and those with non-zero resistance in the wires. Participants explore the implications of resistance on the E field's behavior inside and outside of wires and resistors, as well as the relationship between the E field and current direction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that the E field in a circuit with real (non-zero resistance) wires would still resemble that of an idealized circuit, but with additional E field components inside the wires.
  • Others argue that if the resistance of the wires is not small compared to the resistance of the resistor, the E field lines are not orthogonal to the wires anymore.
  • A participant questions why the E field lines inside the wires would point in the same direction as the current, suggesting it may be due to charge buildup during transient states.
  • Another participant asserts that the E field inside the wire does indeed point in the same direction as the current, while the E field outside the wire has a different orientation.
  • There is a discussion about whether the E field outside the wires is influenced by the E field inside the wires, with some participants expressing uncertainty about the nature of the E field's orientation in different regions.
  • A participant references a paper that provides detailed information about the field lines inside and outside the wire, indicating that it helped clarify some of the questions raised in the discussion.

Areas of Agreement / Disagreement

Participants generally agree that the E field inside the wires points in the same direction as the current. However, there is disagreement regarding the orientation of the E field outside the wires and whether it retains an orthogonal component. The discussion remains unresolved on these points.

Contextual Notes

Some participants express uncertainty about the definitions and implications of the E field's orientation, particularly in relation to Ohmic conductors and the influence of resistance on field lines.

DoobleD
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When looking at the E field in a circuit, we usually find something like the images below (from here).

fig5.gif


voltagee.gif
This is with an idealized circuit, with idealized (0 resistance) wires linked by a resistor. I wonder what the same pictures would look like with real (non 0 resistance) wires?

I think it would be the same, except that now there would also be a E field inside the wires. Is this correct ?

However the pictures above do not show any E field inside the resistor, that seems strange to me.

I'm ignoring any transient state.
 
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DoobleD said:
I wonder what the same pictures would look like with real (non 0 resistance) wires?
For typical setups: very similar. If the resistance of the wires is not small compared to the resistance of the resistor, the field lines are not orthogonal to the wires any more.

The magnetic field gets weaker everywhere if the overall resistance in the circuit increases, but its geometry does not change.
DoobleD said:
However the pictures above do not show any E field inside the resistor, that seems strange to me.
Probably just a drawing issue. You also don't see field lines in the power source.
 
Thank you.

mfb said:
If the resistance of the wires is not small compared to the resistance of the resistor, the field lines are not orthogonal to the wires any more.

Why is that?

Also, can you confirm that the E field lines inside the (non ideal) wires points in the same direction as the current does? Due to some buildup of charges during transient state from what I read.
 
DoobleD said:
Why is that?
You get a component along the wire from the electric field along the wire.
DoobleD said:
Also, can you confirm that the E field lines inside the (non ideal) wires points in the same direction as the current does?
It does not, there is still the orthogonal component.
 
mfb said:
It does not, there is still the orthogonal component.
Are you talking about something besides an Ohmic conductor?
 
mfb said:
You get a component along the wire from the electric field along the wire.

Is this component along the wire inside or outside the wire or both? And where does that component comes from?

Are you saying that an E field inside the wire tends to be parallel to it, while an E field outside tends to be orthogonal to it, so the addition of both make a net E field not quite orthogonal nor parallel, but kind of "tilted" ?
 
mfb said:
No.
Well, if it is Ohmic then by definition ##J=\sigma E##, so I would say that the E field lines do point in the same direction as the current.
 
In the interior of the cable, right.
Not outside (=where the sketch has been drawn), but I misread the question.
 
  • #10
DaleSpam said:
Well, if it is Ohmic then by definition ##J=\sigma E##, so I would say that the E field lines do point in the same direction as the current.

mfb said:
In the interior of the cable, right.
Not outside (=where the sketch has been drawn), but I misread the question.

Thanks. Why then is the outside field not orthogonal anymore? Is it somehow "influenced" by the straight field inside the wires?
 
  • #11
mfb said:
In the interior of the cable, right.
Not outside (=where the sketch has been drawn), but I misread the question.
OK, that makes sense.

@DoobleD inside the wire the current t is in the same direction as the E field. Outside the wire there is no current.
 
  • #12
DoobleD said:
Thanks. Why then is the outside field not orthogonal anymore? Is it somehow "influenced" by the straight field inside the wires?
What do you mean by "not orthogonal"? I am not sure what you are asking.
 
  • #13
DaleSpam said:
What do you mean by "not orthogonal"? I am not sure what you are asking.

Well I'm reusing the term of mfb. I understand it as "not perpendicular". That would mean that the E field just outside the wires has a non zero component along the wire.

I might have misunderstood mfb answer.

I understand that there is no current outside of the wires. My concern is about the E field everywhere. We all agree the E field inside the wires is in the same direction as the current. What about the E field outside the wires?
 
  • #15
DaleSpam said:
You might like this reference. It goes into considerable detail about the field lines inside and outside the wire.

http://depa.fquim.unam.mx/amyd/arch...ia_a_otros_elementos_de_un_circuito_20867.pdf

Thank you, that is exactly what I was looking for!

Reading it, as well as some other papers referenced on it, provided a lot of answers, not only regarding the E field behaviour but also energy flow and surface charges on wires. Actually you already gave me the link but I needed to learn about magnetic fields and the Poynting vector. Very nice. :)
 
  • #16
Yea, it is a really good paper, but definitely assumes some background knowledge to begin with.
 

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