Why is the E-field inside a conductor zero?

[diazona]

OK, in that case:

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

Answer: when the conductor is not in electrostatic equilibrium.

For a perfect conductor (zero resistance), the answer is "never."

 

[flyingpig]

Okay, then what does it mean to have resistance then? This me picturing what's happening to a conductor.

Charges are in side, plus and minuses. The cancel out each other as the net charge becomes zero. The other charges hiding something inside the conductor goes up to the surface to spread the net E-field out.

 

[diazona]

Okay, then what does it mean to have resistance then?

At a microscopic level, it means that the charge carriers bump into things as they move, which makes them lose some energy. This means that in order to keep a constant current flowing, you need to replenish the energy of the charge carriers. To do that, they need to experience a force, and this force is a consequence of the electric field.

This me picturing what's happening to a conductor.

Charges are in side, plus and minuses. The cancel out each other as the net charge becomes zero. The other charges hiding something inside the conductor goes up to the surface to spread the net E-field out.

Sorry, but I can't make any sense of that.

 

[flyingpig]

Sorry, but I can't make any sense of that.

Let's say I have a conductor. Inside it has three charges. Two charge are positive +Q and one of them is negative -Q

When electrostatic equilibrium is established (which is always for ideal conductors) that means one of the positive charge and negative charge are attracted to each other and they give a net charge of 0. The other positive charge that's got nothing to cancel will

1) Magically move to the surface of the conductor because my textbook says so without any intuitive understanding whatsoever and give the entire conductor a net charge of +Q

2) ORRR, if this is a non-ideal conductor, that +Q positive charge would hide inside the conductor and give a E-field of its own inside the conductor and not move up

 

[diazona]

Are you talking about a conductor with three point charges embedded within the conducting material, in some manner that allows them to move around freely within the conductor?

When electrostatic equilibrium is established (which is always for ideal conductors) that means one of the positive charge and negative charge are attracted to each other and they give a net charge of 0. The other positive charge that's got nothing to cancel will

1) Magically move to the surface of the conductor because my textbook says so without any intuitive understanding whatsoever and give the entire conductor a net charge of +Q

2) ORRR, if this is a non-ideal conductor, that +Q positive charge would hide inside the conductor and give a E-field of its own inside the conductor and not move up

Well, choice (1) is clearly kind of silly: physical objects won't do anything just because your textbook tells them to

In any case, I think you're looking at this the wrong way. Remember that the conductor has an infinite number of infinitesimal charges that can move around. The three point charges you've identified are not going to act in the way you've been told that charges in a conductor act, because those three point charges do not constitute a conductor.

I'm not 100% sure about this, but I think what would happen is that the infinitesimal free charges (not your +Q and -Q) which are able to move around inside the conductor would arrange themselves in a layer around each of your three point charges. So for example, each of the two +Q charges would be surrounded by a shell of negative charge, and the layer together with the point charge would form a neutral object. Similarly, the -Q charge would be surrounded by a shell of positive charge, and together they would form a neutral object.

Now, suppose the conductor was originally neutral. Since it has had to create 2 shells of negative charge but only 1 of positive charge, that means it has 1 shell worth of positive charge - a total amount of +Q - that doesn't have anything to surround. That positive charge will try to spread itself out as much as possible, because like charges repel, and that will lead to it distributing itself over the outer surface of the conductor.

 

[flyingpig]

The three point charges you've identified are not going to act in the way you've been told that charges in a conductor act, because those three point charges do not constitute a conductor.

What does that mean? This is just mainly for understanding this concept, we don't have to be dead on exact here.

that will lead to it distributing itself over the outer surface of the conductor.

Why can't they just keep repelling one another isnide the conductor?

 

[flyingpig]

Actually I just have a question, can you even place a point charge inside a hollow conductor? Let us assume all the conductors we are going to talk about is a spherical.

 

[SammyS]

Actually I just have a question, can you even place a point charge inside a hollow conductor? Let us assume all the conductors we are going to talk about is a spherical.

You can do it conceptually.

To do it in practice, you would need to have the charge isolated from the conductor by some insulating material.

 

[diazona]

What does that mean? This is just mainly for understanding this concept, we don't have to be dead on exact here.

I was just pointing out that a conductor consists of an infinite number of infinitesimal mobile charges. The three point charges you're talking about are not infinitesimal, and there are not an infinite number of them. So for example, when one says that the charges in a conductor move to a surface, that does not apply to the three point charges.

Why can't they just keep repelling one another isnide the conductor?

Roughly, because there is nothing holding them inside the conductor.

 

[flyingpig]

I feel like we are going no where with this...

Let me just ask you this.

Since E = 0 inside the conductor, are there any charges inside? Does Gauss's Law just say that the net charge inside is 0? Does it make any conclusion whether

1. Yes there are still charges inside, but their net charge is 0

2. No, all it means is that there is simply no charges inside. It has nothing to do with the sign of the charges

 

[diazona]

Since E = 0 inside the conductor, are there any charges inside? Does Gauss's Law just say that the net charge inside is 0?

Yes, it does.

Does it make any conclusion whether

1. Yes there are still charges inside, but their net charge is 0

2. No, all it means is that there is simply no charges inside. It has nothing to do with the sign of the charges

Gauss's law does not tell you whether #1 or #2 is the case. It only tells you that the net charge is zero.

The definition of a conductor requires that #1 be true, i.e. that there are charges inside the conductor. In order for the conductor to conduct current, there must be mobile charges that can carry that current.

 

[Idoubt]

I remember having the same doubt and running around it for a while so don't get discouraged by it flyingpig.

I will tell you how I understand it.

First what is a conductor

well a conductor is a material which has highly mobile charges, which means that if I apply even a small electric field to it, charges go flying in the direction of the electric field

*( here i mean positive charge though actually in a conductor electrons will move in the direction opposite to the field, but this is not important to us)*

Now what happens when I apply an electric field to a conductor?

Well exactly what we expect, charges go flying in the direction of the field

( if you look at figure 24.16 of the page you posted on page 3 of this thread you can see that this is exactly what happened.)

Of course my conductor was neutral to begin with and no charge has left the conductor so it should still be neutral as a whole.

Since the electrons have moved to one side of the conductor, there are ions or positive charges on the other side.


As more electrons move towards the (now) negative side of the conductor, more positive charges are formed on the other side. now an electron in the middle of the conductor is confused, there is an external electric field telling it to go to one side of the conductor ( the negative ), but now there are positive charges pulling it to the other side so the electron decides to stay STILL.

If something is not moving we know that the net force on it is zero right? and electric field is nothing put force per unit charge. so we can say the external electric field is canceled by a kind of internal electric field created by the pilling up of charges on one side of the conductor, so the net electric field inside ( sum of the external and internal ) is zero.

phew* this is getting long, hope you don't get bored :( .

now the problem of how can wires conduct.

well the answer isn't as complicated as you think. We know that the reason there is no electric field inside a conductor is that , if you apply an electric field, charges pile up as I have described and create an opposite internal electric field and they cancel each other out right?

Now imagine the same situation as before, a conductor in an electric field, charges of opposite polarity pile up on each side. But now imagine that when the positive charge piles up on one side, I just take those charges away!

so now there is no internal electric field ( no charge=no field ) and electrons in the middle of the conductor are no longer confused, they just do what the external field wants them to do since i took away the cause of the internal field.

this is precisely what a battery does, if you connect one terminal of a battery to a wire, it won't conduct, because even though there is an electric field ( external) , charges pile up on the other end and create a field ( internal ) which cancels it.

But now if i connect the other end of the battery to the opposite side of the wire, then the piled up charges go into that side of the battery, now there is no pile up because the charges just exit the wire and hence no internal field to cancel the external electric field and the electrons are controlled by the external field which orders them around now as he pleases.

Hope I helped, But i really really hope that I haven't confused you more :)

 

[SammyS]

I remember having the same doubt and running around it for a while so don't get discouraged by it flyingpig.

I will tell you how I understand it.

First what is a conductor?
...

phew* this is getting long, hope you don't get bored :( .

now the problem of how can wires conduct.
...

Hope I helped, But i really really hope that I haven't confused you more :)

fp, This is very good! Study it & see if it helps.

A big thank you to Idoubt.

 

[flyingpig]

I remember having the same doubt and running around it for a while so don't get discouraged by it flyingpig.

I will tell you how I understand it.

First what is a conductor

well a conductor is a material which has highly mobile charges, which means that if I apply even a small electric field to it, charges go flying in the direction of the electric field

Even a small or none. If I don't apply one, they still fly? That's what people have been trying to say to me. It doesn't need an external field for the charges to move.

If something is not moving we know that the net force on it is zero right?

Constant velocity, the charges can move.

so we can say the external electric field is canceled by a kind of internal electric field created by the pilling up of charges on one side of the conductor, so the net electric field inside ( sum of the external and internal ) is zero.

That was the analogy I was trying to get to diazona except I used "3 charges". But in this case again, things went smoothly because had an external E-field. Many conductors never had an E-field apply to it and we claim that the field is 0 inside.

Now imagine the same situation as before, a conductor in an electric field, charges of opposite polarity pile up on each side. But now imagine that when the positive charge piles up on one side, I just take those charges away!

What do you mean "take those charges away", how can you take them away?

so now there is no internal electric field ( no charge=no field ) and electrons in the middle of the conductor are no longer confused,

I thought they are at the ends of the conductor when an external E-field is applied.

this is precisely what a battery does, if you connect one terminal of a battery to a wire, it won't conduct, because even though there is an electric field ( external) , charges pile up on the other end and create a field ( internal ) which cancels it.

I thought that just means the circuit is broken...

 

[SammyS]

If something is not moving, what is its acceleration? ... zero, so the net force on it is zero. He (Idoubt) didn't say that's the only condition for the net force to be zero, he simply said that in this limited case the net force is zero.

 

[diazona]

Even a small or none. If I don't apply one, they still fly? That's what people have been trying to say to me. It doesn't need an external field for the charges to move.

Well, sort of. Yes, charges can move around without an external electric field, but in that case there would have to be an internal electric field, one produced by the charge distribution in the conductor itself. This corresponds to a conductor not being in equilibrium. If there is no electric field, either internal or external, then the charges will not move (or will move at constant velocity, until they hit the edge of the conductor).

That was the analogy I was trying to get to diazona except I used "3 charges".

But it doesn't work with 3 charges. It only works with an infinite number of infinitesimal charges.

 

[slowing down]

now...the simple solution is potential is inversely proportional to radius.so as the radius on the outer side of a conductor is highst.the potential is lowest.so naturallu to acquire minimum potential the charges reside on the outer surface of a hollow conductor.the conductors in general are not hollow so charge is present inside them.that drives the current.

 

[slowing down]

in addition potential of a conductor as a whole is zero.since they are electrically neutral.so.....charges i.e.charge carriers are present inside them

 

[diazona]

now...the simple solution is potential is inversely proportional to radius.so as the radius on the outer side of a conductor is highst.the potential is lowest.so naturallu to acquire minimum potential the charges reside on the outer surface of a hollow conductor.the conductors in general are not hollow so charge is present inside them.that drives the current.

in addition potential of a conductor as a whole is zero.since they are electrically neutral.so.....charges i.e.charge carriers are present inside them

um... huh? That doesn't quite seem to make sense. In any case, the electric potential of a conductor is the same at all points of the conductor.

 

[Idoubt]

Even a small or none. If I don't apply one, they still fly? That's what people have been trying to say to me. It doesn't need an external field for the charges to move.

This is only true for an ideal conductor with zero resistance ( the word ideal says it all)

( incidentally this is the case inside a superconductor )

Constant velocity, the charges can move.

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.

That was the analogy I was trying to get to diazona except I used "3 charges". But in this case again, things went smoothly because had an external E-field. Many conductors never had an E-field apply to it and we claim that the field is 0 inside.

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.

What do you mean "take those charges away", how can you take them away?

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. )

I thought they are at the ends of the conductor when an external E-field is applied.

yes there are charges at the ends of the conductor, but remember there are still atoms in the middle of the conductor.

If I increase the external electric field the balance of internal and external fields is broken (ext is stronger ) , an electron will break away from it's atom and go to the negative side of the conductor, this in turn increases the internal electric field and so again there is balance and in the centre there is no net field.

I thought that just means the circuit is broken...

yes that is what it means, but why shouldn't a broken circuit conduct? after there is an electric field from the positive end of the battery! The reason is of course because of the internal electric field that cancels it.

if we connect the negative end too, the internal field cannot form as it requires charges to accumulate at one end. ( but here they go into the negative side of the battery.)

 

[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.