Why is the E-field inside a conductor zero?

[flyingpig]

Yeah a Gaussian surface inside a conductor encloses a net charge of 0, but that's all we know. We cannot make any conclusion whatsoever that there are charges on the surface.

 

[Idoubt]

ok I think I finally get what you are saying.

Let us now consider a charged conductor.

Also we accept that in an equilibrium state there can be no electric field inside a conductor.

Now we consider a Gaussian surface inside the conductor in the exact shape of the conductor so that it encloses every part of the conductor but the surface.

Since this Gaussian surface is inside the conductor the total electric flux through it is zero. So by Gauss's law, the charge enclosed is also zero. So we conclude that there is no charge in any interior part of the conductor.

Now consider a second Gaussian surface one that encloses the whole conductor (including the surface) . Now since there is a net charge on the conductor, there will be an electric flux though this Gaussian surface. Now we conclude that there has to be charge somewhere on the conductor.

The only way for both these conditions to be satisfied is for all the charge to be on the surface.

 

[flyingpig]

ok I think I finally get what you are saying.

Let us now consider a charged conductor.

Also we accept that in an equilibrium state there can be no electric field inside a conductor.

Now we consider a Gaussian surface inside the conductor in the exact shape of the conductor so that it encloses every part of the conductor but the surface.

Since this Gaussian surface is inside the conductor the total electric flux through it is zero. So by Gauss's law, the charge enclosed is also zero. So we conclude that there is no charge in any interior part of the conductor.

Now consider a second Gaussian surface one that encloses the whole conductor (including the surface) . Now since there is a net charge on the conductor, there will be an electric flux though this Gaussian surface. Now we conclude that there has to be charge somewhere on the conductor.

The only way for both these conditions to be satisfied is for all the charge to be on the surface.

But unless you do that second Gaussian surface you would never know

I was thinking last night about static equilbrium again.

I was imagining what's actually happening to the electrons. I just want to know, do atoms move when their electrons leave them?

Then I thought about once the equilibrium is reached what happens? I mean there still could be electrons inside the conductor, but you might not be able to see them because the protons' charge is canceling them out, is that right?

Then I also looked at the periodic table. I mean just ignoring the gas part, and focusing on the metals side. Is it true that "odd" valence shells on the periodic table makes good conductors?

 

[flyingpig]

Also for a semi-conductor, is it true that it can have a E-field of 0 and it can suddenly become non-zero? How do we determine it? Is it usually E(t)? That is Electric field as a function of time or E'(t)? How E-field changes with time because it is a semi-conductor?

 

[Idoubt]

I was imagining what's actually happening to the electrons. I just want to know, do atoms move when their electrons leave them?

There is probably a small motion because of the other charged particles in the atom, but if you compare the masses of the atom and an electron, you can see that the force that moves the electron is too low to seriously move the atom at any great speed.

Then I thought about once the equilibrium is reached what happens? I mean there still could be electrons inside the conductor, but you might not be able to see them because the protons' charge is canceling them out, is that right?

Yes there will be electrons "hidden" by protons or you can just call these neutral atoms.

Then I also looked at the periodic table. I mean just ignoring the gas part, and focusing on the metals side. Is it true that "odd" valence shells on the periodic table makes good conductors?

To my knowledge this is not true. As you should know all atoms with the exclusion of hydrogen and helium, try to get 8 electrons in their outer most orbit ( apparently this many give a very stable configuration - this is why noble gases are very stable )

atoms do this either by accepting more electrons into their outermost orbit until there are 8 electrons ( eg: chlorine has 7 valance electrons and it accepts one to become stable)

Now conductors are usually atoms with 1-3 electron in the outermost orbit and 8 electrons in the second outermost shell.

So instead of accepting 7-5 more electrons it simply loses 1-3 electron to attain the stable config.

Also for a semi-conductor, is it true that it can have a E-field of 0 and it can suddenly become non-zero? How do we determine it? Is it usually E(t)? That is Electric field as a function of time or E'(t)? How E-field changes with time because it is a semi-conductor?

Perhaps someone else can answer this.

 

[flyingpig]

There is probably a small motion because of the other charged particles in the atom, but if you compare the masses of the atom and an electron, you can see that the force that moves the electron is too low to seriously move the atom at any great speed.

F = ma

$$F_1 = F_2$$

$$m\vec{a}_1 = M\vec{a}_2$$

If M>>m

$$\vec{a}_1 = M\vec{a}_2$$?

Yes there will be electrons "hidden" by protons or you can just call these neutral atoms.

Okay so that's interesting, but what if I make a Gaussian Surface just small enough and just big enough to only enclose that electron? Doesn't that make it so that I don't have a E-field of 0?

To my knowledge this is not true. As you should know all atoms with the exclusion of hydrogen and helium, try to get 8 electrons in their outer most orbit ( apparently this many give a very stable configuration - this is why noble gases are very stable )

Gas can't be conductors right...?

Perhaps someone else can answer this.

With at least 8 pages and 2600 views, I think I drove off everyone in this forum, right Sammy...?

 

[Idoubt]

F = ma

$$F_1 = F_2$$

$$m\vec{a}_1 = M\vec{a}_2$$

If M>>m

$$\vec{a}_1 = M\vec{a}_2$$?

If m is very small you can't just not write it like 0.0001* x is not the same as x

The last step will be a₁ = Ma₂ / m

or a₁ = K * a₂, where K=M/m which is very large since M>>m, so

a₂ is very small compared to a₁

Okay so that's interesting, but what if I make a Gaussian Surface just small enough and just big enough to only enclose that electron? Doesn't that make it so that I don't have a E-field of 0?

yes that's absolutely correct. It is this electric field that attracts the proton to the electron But from a very large distance ( large enough so that a Gaussian surface encloses the whole atom ) the two equal and opposite charges cancel and there is no net E field.

Gas can't be conductors right...?

They can conduct if you ionize them, this is how a fluorescent light bulb works. But noble elements do not undergo any reactions under normal conditions unlike all the other elements.

With at least 8 pages and 2600 views, I think I drove off everyone in this forum, right Sammy...?

I doubt that ;)

 

[flyingpig]

I will fetch SammyS if he will even come back...

 

[SammyS]

I've been away from the computer for most of the last 10 days !

Sure, I'll come back. (Really, I never left.) I knew that you didn't like a remark of mine - I didn't mean to offend, but yes - sometimes my humor ain't too funny to others - so I've been reading PF posts & responding to some & I've been waiting for a good situation to leave a post to you that is obviously very constructive.

I'll look at this thread to see if I can help.

 

[flyingpig]

I've been away from the computer for most of the last 10 days !

Sure, I'll come back. (Really, I never left.) I knew that you didn't like a remark of mine - I didn't mean to offend, but yes - sometimes my humor ain't too funny to others - so I've been reading PF posts & responding to some & I've been waiting for a good situation to leave a post to you that is obviously very constructive.

I'll look at this thread to see if I can help.

No they were funny because it showed me that you did care about me...

 

[SammyS]

...
With at least 8 pages and 2600 views, I think I drove off everyone in this forum, right Sammy...?

I have continued to read it from time to time. Idoubt seems to be keeping up very well.

Now on the 9th page & 130 posts in this thread... What's the question you fetched me for??

 

[flyingpig]

Well first I said

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.

Then I wanted to ask

For a semi-conductor, is it true that it can have a E-field of 0 and it can suddenly become non-zero? How do we determine it? Is it usually E(t)? That is Electric field as a function of time or E'(t)? How E-field changes with time because it is a semi-conductor?

 

[flyingpig]

Please come back

 

[flyingpig]

IDoubt, what exactly happens if you apply a non-zero e-field to a conductor? Does it make the field inside non-zero again?

 

[flyingpig]

Now I am alone...

 

[diazona]

I suppose I can take this up again...

what exactly happens if you apply a non-zero e-field to a conductor? Does it make the field inside non-zero again?

For an ideal conductor: no it does not.

For a real (non-ideal) conductor: yes, but only for a very short time, until the conductor returns to electrostatic equilibrium. Then the field inside is zero again.

 

[flyingpig]

I suppose I can take this up again...

For an ideal conductor: no it does not.

For a real (non-ideal) conductor: yes, but only for a very short time, until the conductor returns to electrostatic equilibrium. Then the field inside is zero again.

So you have to keep up the field to make it non-zero? What happens if you keep it at an alternating frequency? Like pull it in and out?

 

[SammyS]

Well first I said

"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."​

Then I wanted to ask

"For a semi-conductor, is it true that it can have a E-field of 0 and it can suddenly become non-zero? How do we determine it? Is it usually E(t)? That is Electric field as a function of time or E'(t)? How E-field changes with time because it is a semi-conductor?"​

Although the definitions you give for 'real conductors', 'insulators' and 'semi-conductors' can be useful in some situations, they're not very helpful in discussing the 'E-field problem' you're dealing with here. For instance, conductivity is the reciprocal of resistivity, so an insulator (by the above definition) has zero (or very small) conductivity.

For electrostatics problems, the conductor is usually a metal. Metals have the property of having one or more electrons in the 'conduction band' per atom at ordinary temperatures. Even for the case of a metal with high resistivity, these electrons (in the 'conduction band') are relatively free to move, not being associated with any individual atom in particular.

A complete answer for these three types of materials would be extremely long.

 

[diazona]

So you have to keep up the field to make it non-zero? What happens if you keep it at an alternating frequency? Like pull it in and out?

Not quite. Even if you keep the external electric field up at a constant level, the field inside the conductor will drop away to zero. But if you have a constantly changing electric field, such as an EM wave (or AC current), if the frequency of the change is high enough then I suppose you could keep the electric field inside the conductor from settling down to zero.

 

[flyingpig]

Although the definitions you give for 'real conductors', 'insulators' and 'semi-conductors' can be useful in some situations, they're not very helpful in discussing the 'E-field problem' you're dealing with here. For instance, conductivity is the reciprocal of resistivity, so an insulator (by the above definition) has zero (or very small) conductivity.

And that definition is wrong...?

 

[flyingpig]

Not quite. Even if you keep the external electric field up at a constant level, the field inside the conductor will drop away to zero. But if you have a constantly changing electric field, such as an EM wave (or AC current), if the frequency of the change is high enough then I suppose you could keep the electric field inside the conductor from settling down to zero.

Isn't that what's happening in a semi-conductor?

 

[flyingpig]

Will my search for an answer ever end...?

 

[ideasrule]

Isn't that what's happening in a semi-conductor?

I don't think it's wise to start thinking about semiconductors before understanding what happens in a conductor and insulator. Semiconductors are not simply half-way between conductors and insulators; they have many weird and wonderful properties that are too complicated to discuss before you grasp the basics.