Why is the E-field inside a conductor zero?

[flyingpig]

Homework Statement

Oh dear, veterens of PF who have tried to convince me that E = 0 inside conductors, I am having this problem again.

OKay, let's say that "charges do arrange themselves such that the E-field inside a conductor is always zero", then how can wires in circuits work? If the E-field inside the conductor is 0, how can the charges move? How can there be a current?

The Attempt at a Solution

Going in circles

 

[gneill]

The field inside a conducting wire, with an external field applied (end to end) is not zero.

The charges are in motion, and continue in motion, as though they were attempting to level out and nullify the field. But they can't ever accomplish that as long as the external EMF is maintained. New charges enter at one end, and leave by the other. This is why batteries "run down".

 

[Andrew Mason]

The field inside a conducting wire, with an external field applied (end to end) is not zero.

The charges are in motion, and continue in motion, as though they were attempting to level out and nullify the field. But they can't ever accomplish that as long as the external EMF is maintained. New charges enter at one end, and leave by the other. This is why batteries "run down".

Well, the field inside a conductor is practically 0. It is d/dx(IR) where R is the resistance of the wire. In other words the field is the current x resistance of the wire per unit length, the latter being a very small number measured in ohms/metre.

AM

 

[flyingpig]

Well, the field inside a conductor is practically 0. It is d/dx(IR) where R is the resistance of the wire. In other words the field is the current x resistance of the wire per unit length, the latter being a very small number measured in ohms/metre.

AM

I don't understand whaty you mean by current * resistance per unit length, you mean voltage per length? I don't understand what this has to do with 0 field inside the wire?

 

[Andrew Mason]

I don't understand whaty you mean by current * resistance per unit length, you mean voltage per length? I don't understand what this has to do with 0 field inside the wire?

Well, the units of potential are volts (Joules/coulomb). V=IR (Ohm's law). The units of resistance are Potential/current (eg. Volts/Amperes) or Ohms). The field, E, is equal to dV/dx. Since V = IR, E = d(IR)/dx. Since current is the same at all points in the conductor, this means that E = IdR/dx.

dR/dx is simply the resistance per unit length of the conductor which we could call $\rho_L$. So:

$$\vec{E} = \vec{I}\rho_L$$

AM

 

[gneill]

or, succinctly, the units for the electric field are volts per meter.

 

[flyingpig]

The units isn't giving me the intuition as to how charges flow if the E-field inside the conductor is 0? Do they flow outside?

 

[gneill]

The E field inside the conductor when current flows is NOT ZERO.

At least, it's not zero for DC current and low-ish frequency AC currents. If you're interested in some additional physics details when high frequency AC currents are involved, look up "skin effect". This may not be something you'll run across early on in your coursework.

 

[Andrew Mason]

The units isn't giving me the intuition as to how charges flow if the E-field inside the conductor is 0? Do they flow outside?

There is no field in an ideal conductor (ie zero resistance) in a circuit in which current flows. If there is no potential difference (V = IR = I x 0 = 0) there is no field. The field occurs in the resistance.

This is not difficult to understand. If there is no resistance, one does not need a "force" to keep current going through the conductor.

AM

 

[flyingpig]

Wait, if V = 0, how does that mean E = 0? But I am saying that it is the E-field that's driving the charges right? If there is no E-field they aren't going to move.

 

[Andrew Mason]

Wait, if V = 0, how does that mean E = 0? But I am saying that it is the E-field that's driving the charges right? If there is no E-field they aren't going to move.

dV = Edx If dx is not zero but dV is, what does that tell you about E?

Once moving, charges do not need a force to keep them moving if there is no resistance. So no field is needed to keep current flowing in a perfect (ideal) conductor. One is not accelerating the charges; merely keeping the current constant. The force is needed to push then through a resistance. So that is where the field occurs. If the electrons are pushed through a resistor there has to be a field and a potential difference from one end to the other.

AM

 

[flyingpig]

I still don't understand, especially when we are incooperating potential difference into this question. I can see it mathematically, but I have no intuition it for it whatsoever

 

[flyingpig]

Wait, just how could there be a 0 V? There must be a voltage drop if a current runs across the wire (with negligible resistance)

 

[flyingpig]

Also, inside a conductor, the e-field is 0 by definition because you apply an external field. But in many Guass's law problems, there isn't an external field

 

[JaWiB]

Wait, just how could there be a 0 V? There must be a voltage drop if a current runs across the wire (with negligible resistance)

As the resistance goes to zero, the current created by a given voltage increases without bound--so essentially with zero resistance you could have any current regardless of voltage.

I think you have to keep in mind here that the "zero E-field inside a conductor" rule only works in equilibrium. If you have a conductor sitting in a region of zero electric field, then suddenly turn on an electric field, the electrons have to move to cancel out the electric field. With small resistance they can do that much more quickly (look up dielectric relaxation).

 

[JaWiB]

Also, inside a conductor, the e-field is 0 by definition because you apply an external field. But in many Guass's law problems, there isn't an external field

Not sure what you mean by this. External field or not, there should be zero field inside a conductor. That idea does not come from Gauss's law; it just makes Gauss's law more useful

 

[diazona]

The electric field in a conductor is zero in electrostatic equilibrium. If a wire is carrying a current, it is not in electrostatic equilibrium. If the wire is hooked up to a voltage source (like a battery), that prevents it from ever reaching equilibrium.

 

[Andrew Mason]

The electric field in a conductor is zero in electrostatic equilibrium. If a wire is carrying a current, it is not in electrostatic equilibrium. If the wire is hooked up to a voltage source (like a battery), that prevents it from ever reaching equilibrium.

The point is that the E field is very small inside a real conductor with current flowing. E is proportional to the resistance/unit length of the conductor. If it is an ideal conductor with no resistance, the potential difference from one end of the conductor to the other with current flowing will be V = IR = 0. Since $\Delta V = E\Delta x$ the field E must be 0.

AM

 

[flyingpig]

http://www.electron.rmutphysics.com...rs-Serway-Beichne 6edr-4/24 - Gauss's Law.pdf

Go to page 12 of the pdf, it derives why E-field is 0 inside a conductor

Now go to this site I found https://people.ok.ubc.ca/jbobowsk/phys102/phys102%20002%20Midterm%201%20solns.pdf

Go to the last page, there is no external field, how can there be a E-field of 0 inside the conductor?

 

[SammyS]

http://www.electron.rmutphysics.com...rs-Serway-Beichne 6edr-4/24 - Gauss's Law.pdf

Go to page 12 of the pdf, it derives why E-field is 0 inside a conductor

Now go to this site I found https://people.ok.ubc.ca/jbobowsk/phys102/phys102%20002%20Midterm%201%20solns.pdf

Go to the last page, there is no external field, how can there be a E-field of 0 inside the conductor?

I believe that diazona addresses the problem you are having with this concept.

Look at what Serway says in Chapter 27 (Section 3, I think).

In order for current to flow in a conductor having finite conductance, a non-zero E field is required within the conducting material itself. This is not an electrostatic situation.

 

[flyingpig]

Then how am I suppose to know rather it is in electrostatic situation or not

 

[SammyS]

Electrostatics: The charges are stationary -- in equilibrium.

 

[flyingpig]

No, but answer those Gauss's Law problem don't tell you they are static

 

[SammyS]

Is there a circuit? Is there a source of EMF ?

 

[flyingpig]

No...but charges don't just become stationary just because we add a word called eletrcostatics, you need an external field to make them move so that they become 0

 

[flyingpig]

Please i'll be nice

 

[flyingpig]

Please! I've been stuck on this concept for over 3 months now ...

 

[diazona]

What exactly are you stuck on again? I haven't quite been able to follow what the question is since I last posted.

 

[flyingpig]

Why E = 0 inside a conductor.

In my book, the way it was derived, it only happens when you apply an external E-field.

But in many of my HW problems concerning Gauss's law, this "external" field does not exist anywhere, yet they still claim E = 0 inside a conductor

 

[SammyS]

It seems we have a moving target when trying to answer your questions.

 

[flyingpig]

What?

 

[ojs]

http://www.electron.rmutphysics.com...rs-Serway-Beichne 6edr-4/24 - Gauss's Law.pdf

Go to page 12 of the pdf, it derives why E-field is 0 inside a conductor

Now go to this site I found https://people.ok.ubc.ca/jbobowsk/phys102/phys102%20002%20Midterm%201%20solns.pdf

Go to the last page, there is no external field, how can there be a E-field of 0 inside the conductor?

As to the latter problem that you reference here, then there is an external field to the conductor. The conductor is the hollow sphere (hollow being the key point here) of thickness b-a, so the charge at the center creates the external field for the conductor, that external field aligns the charges inside the conductor to oppose the central charge and hence no field inside the conductor.

 

[flyingpig]

What happens if there is no point charges inside?

 

[diazona]

Why E = 0 inside a conductor.

The reason is simply that if the electric field were not zero, the charges would move around due to the force from the electric field. This applies whether or not the electric field is externally generated.

In my book, the way it was derived, it only happens when you apply an external E-field.

I'd suggest checking to see if your book's derivation fails when the external electric field is equal to zero.

 

[ojs]

What happens if there is no point charges inside?

Well, then we are talking about a different scenario. We no longer have electrostatic equilibrium inside the conductor (although outside of it we have equilibrium) and we really can't say much about how it behaves inside, the electrons try to minimize they'r potential each time (the potential is created by the electrons around them, not something from outside) but they will wander since they have thermal energy and hence velocity, sort of a chaotic movement.