Why is the E-field inside a conductor zero?

[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?"

 

[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.)