Why is the E-field inside a conductor zero?

[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.

 

[flyingpig]

Does that mean in a circuit, charges do move under constant velocity? Because they are in equilibrium?

If I were to tell you, I give you a spherical solid conductor and I tell you the net charge is +Q

Then would it be safe to assume the following?

1. Charges do exist inside this conductor, but their net charge is +Q.

2. If their net charge (with the charges still present inside the conductor) is +Q, there is no E-field because they are inside the conductor?

I am confused how part 2 could be true.

 

[SammyS]

...
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.
...

By external field, we usually mean a field which exists prior to the conductor being inserted into the field.

You seem to be referring to problems involving situations in which the charges on and within a conductor produce the field, -- no other field present.

 

[flyingpig]

Then how was I or am I (because the course is over now) suppose to know someone put an external field there and zero'd the field inside?

 

[SammyS]

The problem will state if there is a pre-existing external field.

 

[flyingpig]

No they don't, they never do. All Gauss's Law problems are the same. They give you some symmetrical object, they tell you the net charges and such and you find the E-field inside, outside.

 

[diazona]

Does that mean in a circuit, charges do move under constant velocity?

Within a section of wire where there is zero resistance and no voltage drop, then yes, charges do move at constant velocity. But if that's all there was, it would be a very boring circuit. In practice, a circuit will contain things like resistors and batteries that will cause the charges to accelerate.

If I were to tell you, I give you a spherical solid conductor and I tell you the net charge is +Q

Then would it be safe to assume the following?

1. Charges do exist inside this conductor, but their net charge is +Q.

Yes. Well, technically the charges are on the surface of the conductor.

2. If their net charge (with the charges still present inside the conductor) is +Q, there is no E-field because they are inside the conductor?

There is no electric field (which, again, means E = 0) inside the conductor.

No they don't, they never do. All Gauss's Law problems are the same. They give you some symmetrical object, they tell you the net charges and such and you find the E-field inside, outside.

Then, as SammyS said, there is no external electric field.

Of course, it is possible to create a problem in which there is an external electric field. Here's one classic example:

An electron is placed inside a conducting spherical shell, which carries a net charge of $$4.7\times 10^{-18}\mathrm{C}$$, of inner radius $a$ and outer radius $b$. Find the surface charge density on each surface of the conducting shell.

 

[SammyS]

No they don't, they never do. All Gauss's Law problems are the same. They give you some symmetrical object, they tell you the net charges and such and you find the E-field inside, outside.

Yes, but that's NOT what's usually meant but an external field.

 

[flyingpig]

I don't understand, if there is no need for an external E-field to create electrostatic equilibrium, tthen why did they bother making one to help us understand?

 

[diazona]

I don't understand, if there is no need for an external E-field to create electrostatic equilibrium, tthen why did they bother making one to help us understand?

I don't think they put the external field into help you understand. It doesn't help make their argument any clearer; in fact it's pretty irrelevant.

I believe the reason they mentioned an external electric field is to show you that E = 0 inside a conductor even when the external field is nonzero. Perhaps they thought that if they didn't mention it explicitly, some students would think that the argument only applies to the field produced by the charges in the conductor itself, i.e. that if there were an external electric field, that field would "continue" inside the conductor. But of course, that's not the case; the electric field is always zero inside a perfect conductor (in equilibrium).

 

[flyingpig]

This is getting derailed.

I think a better question now is "Just when is the E-field inside a conductor NOT zero?"