Why is the E-field inside a conductor zero?

[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.

 

[flyingpig]

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.

How could charges move on its own such that it wants to go to equilibrium? I am getting "off-topic" here, but this seems to violate 2nd law of thermodyanmics. Why would charges want equilibrium instead of chaos?

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

If the external field is 0, then there is no external field...

Here is the derivation from my book

[PLAIN]http://img15.imageshack.us/img15/3426/0o0o.jpg

 

[iRaid]

If I remember correctly, isn't it that E=0 inside a coil of wire?

 

[SammyS]

So, are you concerned about the case of a conductor in a region which has no external electric field?

1. I presume that if there is no net charge on the conductor, then it's reasonable to infer that the electric field is zero everywhere. ... Why not?​

2. If there is no external field (any field is only due to the charges in the conductor), but there is a net charge on the conductor, then what?​

 

[flyingpig]

So, are you concerned about the case of a conductor in a region which has no external electric field?

Yes.

1. I presume that if there is no net charge on the conductor​

How do we know this?

then it's reasonable to infer that the electric field is zero everywhere. ... Why not?

Don't understand why is this reasonable

2. If there is no external field (any field is only due to the charges in the conductor), but there is a net charge on the conductor, then what?​

I really don't understand this. If there is no E-field why would the electrons move in such a probabilistic way to find other protons and cancel out to make a net charge and then the other ones magically go on the surface of the conductor.

 

[flyingpig]

If I remember correctly, isn't it that E=0 inside a coil of wire?

Then how can charges travel to make current?

 

[SammyS]

Your response after I asked: "So, are you concerned about the case of a conductor in a region which has no external electric field?"

Yes.

Now, we're getting somewhere regarding pinning down what you're having a problem understanding.

 

[flyingpig]

Yes...let's continue.

 

[SammyS]

There are two possible cases:

1. The conductor has zero net charge.

2. The conductor has a non-zero net charge.
​

Agree?

(You seemed to have a problem with #1 previously.)

 

[flyingpig]

Yes I agree.

 

[SammyS]

For case1: How do you conceive of a situation where there is a non - zero electric field, seeing as the net charge is zero?

Added in Edit:

Maybe I should say: What situation can you conceive of where there is a non - zero electric field, seeing as the net charge is zero?

 

[flyingpig]

Let's say there are three charges of all equal magnitudes. One is negative and the other two is positive.

The positive one cancels out with the negative one but the lonely positive charge will spread its own E-field

 

[SammyS]

In that case, the conductor has a non-zero net charge.

 

[flyingpig]

And then there is a E-field inside.

 

[SammyS]

Stick with one case or the other. I was referring to case #1, No net charge.

 

[flyingpig]

Yeah no net charge, the net charge enclosed is nonzero

 

[diazona]

How could charges move on its own such that it wants to go to equilibrium? I am getting "off-topic" here, but this seems to violate 2nd law of thermodyanmics. Why would charges want equilibrium instead of chaos?

The 2nd law of thermodynamics says that the entropy of the universe can (probabilistically) never decrease. It does not say that any particular physical system will prefer chaos to equilibrium, and it does not say that particles are going to ignore the basic laws of mechanics. Unless you are going to calculate the entropy change of some process, there is no call to invoke the second law of thermodynamics.

If the external field is 0, then there is no external field...

Not really. \mathbf{E} = 0 is a perfectly valid value of an external electric field. When your book says "...in an external electric field E," that includes the possibility \mathbf{E} = 0. So what I was saying was, think through the derivation given in your book and convince yourself that it works even when \mathbf{E} = 0.

 

[flyingpig]

E = 0 means E = 0, it means there is no E-field that's why it is 0??

 

[diazona]

Regardless, I'll say again that "...in an external electric field E" does include the possibility \mathbf{E}=0. It does not mean that E has to be nonzero.

 

[flyingpig]

No it says "...in an external electric field" which implies there is a E-field, E = 0 means there is none, no field.

 

[flyingpig]

PLEASE DON'T GIVE UP ON ME! I know I am stupid but I really need to get this concept handed down

 

[diazona]

No it says "...in an external electric field" which implies there is a E-field, E = 0 means there is none, no field.

Yes, it implies there is an E field, which could be zero. Otherwise it would say "...in a nonzero external electric field."

"No electric field" is just a way of expressing E = 0 in words.

 

[flyingpig]

Okay then, continue. Sigh I feel sometimes I am reading too much into these things.

 

[diazona]

Well perhaps. But anyway: it doesn't matter at all what the external electric field is, whether it's zero or not.

The argument both I and your book (and perhaps others, I forget) have been making is this: suppose the electric field at some point inside the conductor is not zero. Then electrons will be accelerated due to the Coulomb force at that point, meaning that the conductor is not in electrostatic equilibrium. So logically, if a conductor is in electrostatic equilibirum, there cannot be any nonzero electric field at any point inside it.

 

[flyingpig]

But my question was on arriving electrostatic equilibrium. Even if electrostatic equilibirum is achieved, it doesn't mean they have stopped moving. The electrons could still run on constant speed.

Also my exams often have these problems where they expect you assume there is always an external field (whether 0 or not).

Just take an isolated conductor and they ask you find the E-field inside (and outside) of this conductor.

How do we know conductors are in equilibrium or not? Wires aren't in equilibrium right? Because current runs through it.

 

[diazona]

But my question was on arriving electrostatic equilibrium. Even if electrostatic equilibirum is achieved, it doesn't mean they have stopped moving. The electrons could still run on constant speed.

But that wouldn't change the electric field. In electrostatic equilibrium, the charge distribution is constant, by definition. And the electric field is a function of the charge distribution. So if, at some moment the conductor is in electrostatic equilibrium, the electric field will be zero, and since the charge distribution is constant, the electric field will not change from zero.

I actually can't remember whether electrostatic equilibrium means that there are no moving charges at all, or just that there are no accelerating charges. But I don't think it matters for the purpose of proving that electric field is zero inside an ideal perfect conductor in equilibrium. The key property is that the charge distribution is constant.

How do we know conductors are in equilibrium or not? Wires aren't in equilibrium right? Because current runs through it.

According to the definition you were thinking about, in which charges move at constant (possibly zero) velocity, then an ideal wire would be in electrostatic equilibrium. If electrostatic equilibrium means no moving charges at all, then no, it wouldn't. But again, I think in either case we can prove that the electric field inside the wire is zero.

P.S. For a physics problem, you generally assume all conductors are in equilibrium unless told otherwise. In real life, if the conductivity is high enough, you just wait a short time and the conductor will come to equilibrium.