Why is the E-field inside a conductor zero?

[Idoubt]

[URL]http://upload.wikimedia.org/wikipedia/commons/f/f3/Faraday_cage.gif[/URL]

this is the picture of what I have been saying. ( the fact that this is hollow isn't really relevant )imagine that in this picture, electrons enter from the right and leave on the left side, and you see how a battery can make a wire conduct ( that there is an electric field inside the conductor now. )

Also initialy when the electrons are rearranging, there is an electric field inside the conductor, it is only when it reaches that final configuration that there is no field,

A conducting wire is always trying to reach that state but isn't being allowed to do so, because charges are entering one side and leave the other.

 

[flyingpig]

This is only true for an ideal conductor with zero resistance

Then how does it fly without an E-field

Yes, and here there electrons in the middle of the conductor are moving with a constant velocity v = 0 , so net force has to be zero.

Okay, I will accept this part.

this is the case inside a perfect conductor with zero resistance, its sort of like saying that on a frictionless surface you don't need a force to keep an object moving. But in reality all conductors have a small finite resistance, which is negligible, but that's not what you were asking about i think.

No my question was this.

But is this what's happening?

You get minus and plus charges inside a conductor. They can move freely so plus and minus are attracted to each other and they cancel out. The remaining charges who are free from NOT canceling out repel each other.

I don't know what the probability distribution is for them inside the conductor, but how come they all end up on the surface? Is it possible that some are hiding and not 'canceling' out?

i will answer the other posts and quotes tomorrow.

 

[Idoubt]

Then how does it fly without an E-field

there is random motion due to thermal agitation but, charges do not move in a specific direction without and electric field

You get minus and plus charges inside a conductor. They can move freely so plus and minus are attracted to each other and they cancel out. The remaining charges who are free from NOT canceling out repel each other.

Here you are are talking about a CHARGED conductor and not a conductor in an electric field right? If so yes that is the case.

I don't know what the probability distribution is for them inside the conductor, but how come they all end up on the surface? Is it possible that some are hiding and not 'canceling' out?

the charges all want to get away from each other and being on the surface is the way to achieve this

 

[flyingpig]

well the charges are all pushed to one side of the conductor right? I take a wire and connect it between that side and the Earth and all those charges just flow out ( this is the same as connecting the negative end of the battery. )

Grounding? I see

Here you are are talking about a CHARGED conductor and not a conductor in an electric field right? If so yes that is the case.

I thought it doesn't matter, the E-field is still 0 inside?

the charges all want to get away from each other and being on the surface is the way to achieve this

Why can't they keep repelling each other inside?

So was my idea right though?

 

[Idoubt]

I thought it doesn't matter, the E-field is still 0 inside?

yes it is zero in both cases, but you mentioned 'charges that do not cancel' so I thought you may have meant a charged conductor, did you?

Why can't they keep repelling each other inside?

Ok let's put a charge +q inside a conductor. what is going to happened? Well the electrons immediately around our charge are going to move closer towards it right? this leaves a slightly positive charge where the electrons came from. Now electrons from even further out come closer to fill this electron deficiency, but this again leaves a positive charge even further out. So the positive charge is sort of radiating outward from our charge +q.

this process continues until the positive charge hits the surface. now there are no more electrons that are even further out that can come and neutralize the positive charge, and so the surface of the conductor now has a positive charge!

So was my idea right though?

Why don't you tell me what your idea is now, be clear about your conditions and predicit how the charges will behave and why.

 

[flyingpig]

yes it is zero in both cases, but you mentioned 'charges that do not cancel' so I thought you may have meant a charged conductor, did you?

Sorry I am laggnig so bad lately.

A charged conductor is one that has a non-zero charged right? If so yeah.

Ok let's put a charge +q inside a conductor. what is going to happened? Well the electrons immediately around our charge are going to move closer towards it right?
this leaves a slightly positive charge where the electrons came from.
, but this again leaves a positive charge even further out. So the positive charge is sort of radiating outward from our charge +q.

And this happens instantaneously?

this process continues until the positive charge hits the surface.

You mean the +q we placed in the center? How does that work? I thought it won't move anymore now that the charge be is being cancled out by the electrons

Why don't you tell me what your idea is now, be clear about your conditions and predicit how the charges will behave and why.

Let's just say I have an empty conductor, with nothing. Suddenly I place a +q charge inside

If I draw field lines, the E-field is radially outwards.

So there is a field inside.

Now you are telling me that the empty (or I guess "neutral") conductor would split into + and - charges. The minus charges run to that +q charge inside the conductor to cancel out the net charge. The other plus charges again come back to equilibrium by canceling out the other minus charges that doesn't cancel out. But there is one extra + charge that didn't cancel out because there is "odd" number of + and - charges. So that conductor is +q net charge on the surface?

Now my question is, can there be an unpaired charge in which it DOESN'T cancel out

 

[SammyS]

"(Quote from Idoubt
Ok let's put a charge +q inside a conductor. what is going to happened? Well the electrons immediately around our charge are going to move closer towards it right?
this leaves a slightly positive charge where the electrons came from.
, but this again leaves a positive charge even further out. So the positive charge is sort of radiating outward from our charge +q.
"

And this happens instantaneously?

If you look at the Text you posted in Post #36 of this thread, you will see that this typically takes on the order of 10^-16 seconds .

 

[flyingpig]

Then why do we need an external e-field in the first place?

Could you continue elaborating how charges run inside a 0-field isnide a conductor?

 

[SammyS]

We don't NEED an external field.

I'm pretty sure that Serway is saying that even in the case where we place a neutral conductor into a region in which an E field already exists, that the E field inside the conductor will be zero - after about 10^-16 seconds.

I doubt that he considered that anyone would expect a neutral conductor to have a non-zero E-field for the case that there are no charges present and no pre-existing E-field present.

 

[Idoubt]

And this happens instantaneously?

yes practically instantaneously since electrons are really really fast.

You mean the +q we placed in the center? How does that work? I thought it won't move anymore now that the charge be is being cancled out by the electrons

No, not the +q at the center, but now the surface has a positive charge due to electron deficiency ( electrons moved towards the center to cancel out +q)

But there is one extra + charge that didn't cancel out because there is "odd" number of + and - charges. So that conductor is +q net charge on the surface?

yes but remember that this +q charge is distributed evenly over the entire surface, not one positive ion sitting somewhere on the surface of the conductor. ( the induction takes care of this, the electrons near the surface will be shifted a little towards the center so they don't cancel the positive charge of the ion completely, so there is a small positive charge associated with every atom on the surface and all these small charges add upto +q)

Now my question is, can there be an unpaired charge in which it DOESN'T cancel out

The only place charge will not cancel out is at the surface because there is no further supply of charges from further out.

 

[flyingpig]

https://www.youtube.com/watch?v=BcuQ2c_WrMc


In the beginning, Walter Lewin says there are no charges inside. Doesn't this contradict what we talked so far? That there are charges inside, but their net charge happens to be 0?

 

[SammyS]

Obviously Professor Lewin is talking about the net charge. I'm sure he knows that the metal shell is made up of atoms whose make up includes charged particles - some positive and some negative. It would have been nice if he had said zero net charge or had said the interior was uncharged rather than to say there are no charges there.

Added in Edit:

At about the 48 second mark, Professor Lewin makes a misstatement. He says that a charge of -3Q is on the outer surface of
the shell. However, the rest of his solution makes if clear that the net charge on the shell is -3Q, -2Q of that being on the outer surface, -Q being on the inner surface.

 

[Idoubt]

In the beginning, Walter Lewin says there are no charges inside. Doesn't this contradict what we talked so far? That there are charges inside, but their net charge happens to be 0?

as Sammy said, Prof Lewin means the net charge. ( After all, all matter usually has electrons and protons)

Also at 01:26 he says the if there was an electric field inside the conductor, the electrons (charges) would move in such way as to kill it

This is precisely what we were talking about ( charges piling up to kill the E field)

 

[flyingpig]

Let's try to see this using atoms.

Some atoms have excess e^-, some don't.

Now I am guessing those electrons that aren't bounded to their nucleus gets to move around and neutralize other atoms? And this supposingly happens instantaneously?

 

[SammyS]

Probably not instantaneously. The excerpt for your textbook (Post #36 of this thread) says a good conductor reaches equilibrium in a time on the order of 10^-16 seconds.

 

[Idoubt]

Let's try to see this using atoms.

Some atoms have excess e^-, some don't.

Now I am guessing those electrons that aren't bounded to their nucleus gets to move around and neutralize other atoms? And this supposingly happens instantaneously?

atoms of a neutral conductor won't have excess e^-s, only a charged conductor will have excess or shortage of e^-s

For conductors the electrons in the outermost shell are extremely loosely bound and they move from atom to atom randomly through thermal agitation.

so put a charge somewhere inside the conductor and the loosely bound e^-s come running towards/away from it

How fast it does this can be figured out if you know the charges and distance between them, ( to actually calc this is kind of complicated cos there are a lot of factors which are unimportant to our discussion ) and as your text says it takes 10^-16 seconds on an average, this for all practical purposes is instantaneous.

To give you a feel for that time, light that travels 300,000 km per second, will travel 30 nano meters in that time.
That's like 300 atoms in a line

So the time is absurdly small.

 

[flyingpig]

I know none of you are in the position to answer this but do you thinks I finally understand it? I think I do, but it's just that in class my professor and many others often confuse me when they don't understand the concept of "net charge" as opposed to "nothing (charges) inside"

 

[flyingpig]

Also, now that I jussst started on surface integrals, is this the REAL Gauss's Law?

\varepsilon_0\;\iint_S\!\!\!\!\!\!\!\!\!\!\!\!\!\!\bigcirc \mathbf{E}\; \cdot\; \mathbf{dS}= \sum Q_{enclosed}

I am really opposed to people using "q_inside" and "dA"

 

[diazona]

I know none of you are in the position to answer this but do you thinks I finally understand it? I think I do, but it's just that in class my professor and many others often confuse me when they don't understand the concept of "net charge" as opposed to "nothing (charges) inside"

They probably do understand the distinction. It's just that you're not using the same definitions they do. That's fine as long as you can "translate" what other people are saying from their terminology to yours. When someone talks about a conductor with no charge inside it, for example, you should know that they mean no net charge, because if there were no charged material at all, it wouldn't be a conductor.

Also, now that I jussst started on surface integrals, is this the REAL Gauss's Law?

\varepsilon_0\;\iint_S\!\!\!\!\!\!\!\!\!\!\!\!\!\!\bigcirc \mathbf{E}\; \cdot\; \mathbf{dS}= \sum Q_{enclosed}

I am really opposed to people using "q_inside" and "dA"

That is one way to write the integral form of Gauss's law, but only if the enclosed charges are all point charges (and only in a vacuum). The most general form, using your notation, would be
\epsilon\iint_S\!\!\!\!\!\!\!\!\!\!\!\!\!\!\bigcirc \mathbf{E}\cdot\mathrm{d}\mathbf{S} = \iiint_V\rho\,\mathrm{d}V
Here \epsilon is the permittivity of the material that fills the volume V. If the region is filled with nothing (vacuum), it's equal to the electric constant \epsilon_0.

 

[Idoubt]

well my advice is to keep thinking about it till you yourself are satisfied, look at the applications of the law to get a better feel for it. Sometimes you have to understand the same thing from 2 or 3 different angles before you are fully satisfied :)

 

[flyingpig]

Now that I think I understand conductors here are my new questions

1) If a conductor has a net "positive" or "negative" charge, it just means an excess of protons or electrons right? Or a dominance of one over the other.

2) If a conductor has a net charge is 0 then

2i) There is an equal amount of protons and electrons

2ii) The conductor inside still has a net charge of zero and there isn't enough electrons or protons to go out on the surface. In other words, if a conductor has a net charge of 0, then you can't conclude whether there are electrons and protons on the surface.

3) What exactly does it mean for a 'charged' and an 'uncharged' conductor mean?

4) Remember when we were talking about resistance in the conductor and how only ideal conductors have 0 field inside? Does that mean real conductors (non-ideal) does NOT take 10^-16 seconds to reach electrostatic equilibrium? Is that what it means for real conductors?

5) Also \varepsilon_0\;\iint_S\!\!\!\!\!\!\!\!\!\!\!\!\!\! \bigcirc \mathbf{E}\; \cdot\; \mathbf{dS}= \sum Q_{enclosed}, I just want to ask. In my physics class, we say that Gauss's Law only holds for symmetric surfaces, but this integral doesn't seem to suggest it only works for symmetric objects. Isn't this just a vector field dotting a surface area element?

 

[Idoubt]

1) If a conductor has a net "positive" or "negative" charge, it just means an excess of protons or electrons right? Or a dominance of one over the other.

This is fundamentally correct. It might be worth remembering however that in a metal it is always an excess or deficiency of electrons that decide the charge. ( because you can't remove protons without nuclear reactions )

2) If a conductor has a net charge is 0 then

2i) There is an equal amount of protons and electrons

yes that is correct.

2ii) The conductor inside still has a net charge of zero and there isn't enough electrons or protons to go out on the surface. In other words, if a conductor has a net charge of 0, then you can't conclude whether there are electrons and protons on the surface.

A better way to say it would be that there would be an equal number of electrons and protons EVERYWHERE, so that of course includes the surface.

3) What exactly does it mean for a 'charged' and an 'uncharged' conductor mean?

Could you explain this question some more?

4) Remember when we were talking about resistance in the conductor and how only ideal conductors have 0 field inside? Does that mean real conductors (non-ideal) does NOT take 10^-16 seconds to reach electrostatic equilibrium? Is that what it means for real conductors?

Ideal conductors have no RESISTANCE. This means that an electron if it is moving, will keep moving forever ( like frictionless surface). I don't think ideal conductors are relevant to our discussion.

Real conductors will have a 0 field once they reach electrostatic equilibrium ( not before) and it takes about 10^-16 seconds for them to reach electrostatic equilibrium.

5) Also \varepsilon_0\;\iint_S\!\!\!\!\!\!\!\!\!\!\!\!\!\! \bigcirc \mathbf{E}\; \cdot\; \mathbf{dS}= \sum Q_{enclosed}, I just want to ask. In my physics class, we say that Gauss's Law only holds for symmetric surfaces, but this integral doesn't seem to suggest it only works for symmetric objects. Isn't this just a vector field dotting a surface area element?

You are absolutely correct, Gauss's law is once of the four fundamental laws of electromagnetic theory ( there are 4, called Maxwell's equations) and they are true everywhere.

The reason we are concerned with symmetry is that, Gauss's law is only useful for finding the electric field if we have some sort of symmetry, otherwise the surface integral is very complicated ( you have to take the dot product of the electric field and the surface element for every point on the surface, this is complicated for an irregular surface )

But if we take our Gaussian surface in such a way that the electric field is constant for parts on the surface and usually parallel or perpendicular to the surface elements, then we can forget about the dot product and take the electric field outside the integral, and just integrate the surface.

If you look at Gauss's law problems you will see that we always choose a Gaussian surface such that the electric field is parallel or perpendicular at all points of our surface, and usually a constant too.

 

[flyingpig]

This is fundamentally correct. It might be worth remembering however that in a metal it is always an excess or deficiency of electrons that decide the charge. ( because you can't remove protons without nuclear reactions )

Is it equally correct to say "an excess of charged atoms over neutral atoms"

A better way to say it would be that there would be an equal number of electrons and protons EVERYWHERE, so that of course includes the surface.

But is my deduction right?

Could you explain this question some more?

what is a charged conductor? What is an uncharged conductor?

Ideal conductors have no RESISTANCE. This means that an electron if it is moving, will keep moving forever ( like frictionless surface). I don't think ideal conductors are relevant to our discussion.

Real conductors will have a 0 field once they reach electrostatic equilibrium ( not before) and it takes about 10^-16 seconds for them to reach electrostatic equilibrium.

Yeah, I mean can we take the Earth as a conductor?

I mean electrons in ideal conductor only stop moving when they reach equilibrium which takes place almost instantaneously.

Real conductors also take place instantaneously

But I am asking whether if Real Conductor's "instantaneous time" > Ideal Conductor's "instantaneous time"

The reason we are concerned with symmetry is that, Gauss's law is only useful for finding the electric field if we have some sort of symmetry, otherwise the surface integral is very complicated ( you have to take the dot product of the electric field and the surface element for every point on the surface, this is complicated for an irregular surface )

It isn't that complicated, it's just tedious sometimes.

But my question concerns whether it still holds for non-symmetric surfaces.

 

[Idoubt]

Is it equally correct to say "an excess of charged atoms over neutral atoms"

No, because only the charged atoms matter, how many neutral atoms there are are irrelevant.

But is my deduction right?

Well i think your deduction kind of has the cart in front of the horse, If there is no net charge, there is no electric field and we don't even have to think about electric fields pushing charges to the surface.

what is a charged conductor? What is an uncharged conductor?

A conductor is a material whose valance electrons are extremely loosely bound to the atoms ( so much so that even thermal agitation can free it) and hence it conducts electricity with ease.

A charged conductor is one which has excess or insufficient electrons compared to protons.
( from our discussion we know that such conductors will have all the charge at the surface. The surface will have an excess of e^-s or a deficiency of e^-s )

An uncharged conductor or neutral conductor is one in which there are an equal number of electrons and protons

Yeah, I mean can we take the Earth as a conductor?

No i believe the resistance of the Earth is very high compared to typical conductors say copper or silver, so it cannot be called a conductor

I mean electrons in ideal conductor only stop moving when they reach equilibrium which takes place almost instantaneously.

Real conductors also take place instantaneously

But I am asking whether if Real Conductor's "instantaneous time" > Ideal Conductor's "instantaneous time"

I would say yes, because for the same charge configuration ( hence the same electric field strength) more charge will flow in the case of an ideal conductor due to zero resistance

It isn't that complicated, it's just tedious sometimes.

But my question concerns whether it still holds for non-symmetric surfaces.

hmm I don't know, trying to find the electric field due to a charged sphere with a square Gaussian surface seems pretty complicated to me.

But to answer your question yea it holds for ANY closed surface.

 

[flyingpig]

No, because only the charged atoms matter, how many neutral atoms there are are irrelevant.

So a conductor would still be considered as charged if # charged atoms < # neutral atoms

Well i think your deduction kind of has the cart in front of the horse, If there is no net charge, there is no electric field and we don't even have to think about electric fields pushing charges to the surface.

So I am right...?

An uncharged conductor or neutral conductor is one in which there are an equal number of electrons and protons

Is there actually such thing as atoms with only the neutron?

I would say yes, because for the same charge configuration ( hence the same electric field strength) more charge will flow in the case of an ideal conductor due to zero resistance

Alright, here is what I want to really set the definitions here now.

Does that mean "real conductors" (as one with resistance) that

1. Insulators is a conductor with infinite (or very big) resistance
2. Semi-conductors are conductors with a moderate resistance

In other words, everything is a conductor.

 

[Idoubt]

So a conductor would still be considered as charged if # charged atoms < # neutral atoms

Yes. The easiest way to define it would be to say that a conductor is charged when

# protons is not equal to # electrons.

So I am right...?

If you are saying there is no net charge on the surface on an uncharged conductor you are right. I'm still not sure why you are asking this though.

Is there actually such thing as atoms with only the neutron?

No. Neutrons are just that... neutrons. To my knowledge they never bond without protons.

Alright, here is what I want to really set the definitions here now.

Does that mean "real conductors" (as one with resistance) that

1. Insulators is a conductor with infinite (or very big) resistance
2. Semi-conductors are conductors with a moderate resistance

In other words, everything is a conductor.

Yes to all the above. But 'everything' cannot be called a conductor, a material with charged particles can be called a conductor in the way you defined ( ie insulators being conductors with high resistance) and most things we encounter do fall into that category.
But I think there can be exceptions eg: a neutron star ( made up neutrons )

But keep in mind conductors are defined in reality as materials with a low resistance.

 

[flyingpig]

Yes. The easiest way to define it would be to say that a conductor is charged when

# protons is not equal to # electrons.

Just want more ways to explain one thing because that's physics!

If you are saying there is no net charge on the surface on an uncharged conductor you are right. I'm still not sure why you are asking this though.

I just think it is important for that clarification because I think most people wouldn't be able to realize that. It's like saying if the flux is 0, that means there is no presence of field, which is totally wrong.

If you take the enclosed net charge inside a conductor and it turns out to be 0, you really can't make any conclusion that there are charges that will go to the surface. For all we know, it could just so happen that there is an equal amount of electrons and protons inside the conductor to make that 0 net charge.

Yes to all the above. But 'everything' cannot be called a conductor, a material with charged particles can be called a conductor in the way you defined ( ie insulators being conductors with high resistance) and most things we encounter do fall into that category.
But I think there can be exceptions eg: a neutron star ( made up neutrons )

Ohh so there is such thing as "atoms with only neutrons"...?

 

[Idoubt]

I just think it is important for that clarification because I think most people wouldn't be able to realize that. It's like saying if the flux is 0, that means there is no presence of field, which is totally wrong.

If you take the enclosed net charge inside a conductor and it turns out to be 0, you really can't make any conclusion that there are charges that will go to the surface. For all we know, it could just so happen that there is an equal amount of electrons and protons inside the conductor to make that 0 net charge.

If the net charge of a conductor is zero, then we can form the conclusion that there is NO charge on the surface ( as long as there is no external field ), by using the word 'net' charge we already take into account the no of protons and electrons so we needn't mention them separately.

Ohh so there is such thing as "atoms with only neutrons"...?

No they aren't atoms. It's just neutrons. Atoms by definition are positive nuclei surrounded by negative charge, and atomic bonds are electrostatic.

Neutrons are uncharged so they cannot be involved in forming molecules etc so they are not atoms.

 

[flyingpig]

If the net charge of a conductor is zero, then we can form the conclusion that there is NO charge on the surface ( as long as there is no external field ), by using the word 'net' charge we already take into account the no of protons and electrons so we needn't mention them separately.

Nah I just mean the inside

 

[Idoubt]

Nah I just mean the inside

I'm still not sure what distinction or definition you are trying to make here. Are you saying that with a Gaussian surface inside the conductor you cannot say whether there are charges on the surface?