# Why there is no electric field inside a conductor in electrostatics?

## Main Question or Discussion Point

I know an argument that i don´t like. It say´s:
If there were electric field inside a conductor in electrostaic equilibrium, it would excert force on the charges and move them.
But this argument implies that there are infinite charges inside the conductor. This is not very plausible, if charges have mass.

## Answers and Replies

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guilcosa,

You could answer this question easily by a simple "back of the enveloppe" calculation.

Assume you have a plate of metal, say iron.
Assume you displace all the free electrons from a 1-atom-thickness on one side to the other side.
Calculate the charge densities on the surfaces.
Calculate the electric field inside the plate.

I expect you to find an enormous electric field.
This means that the reaction of a conductor to real-life electric fields should only involve a tiny fraction of the charge available in a thin 1-atom layer of iron. This means that the depletion of free electrons would affect the physics of conductors only in extreme-extreme conditions. Enormous forces would be at play and the material would probably explode.

I expect this result because it is known that the "Coulomb" is an enourmous electrical charge and that it corresponds to the charge of less than a mole of electrons (1E-5 moles actually).

In other words: real life electric fields and voltages are always created by a very small fraction of the available electrons.

Still other words: electric fields in laboratories are always very small compared to electric fields on the atomic scale, really very small.

Why is this so? Simply because materials are are "assembled" by electrical forces.
Experiences in electrostatics rarely stress a material very much, specially dense materials.
There are exceptions: disruptions in gases, lightnings, laboratory plasmas ...

Michel

PS:

It could be interresting to refine such a calculation.
How many free electrons per atoms are there in Iron?
Should we expect that only one layer of atoms make this story or would more layers be involved?
Could it be possible to modelise the penetration of a static electric field in the conductor?

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I just realized that you could picture it faster.

Take a capacitor with a given voltage.
Calculate the charge on its plates in Coulombs.
Convert that in a number of electrons.
Compare this number of electrons to the number of atoms in the plates or to the number of atoms at the surface of the plates.

Conclude!

Michel

guilcosa said:
I know an argument that i don´t like. It say´s:
If there were electric field inside a conductor in electrostaic equilibrium, it would excert force on the charges and move them.
But this argument implies that there are infinite charges inside the conductor. This is not very plausible, if charges have mass.

There are many electric fields inside a conductor...the reason there is no "net" electric field is because the charges balance themselves in such a way to cancel the overall electric field.

As far as "electrostatic equilibrium" is concerned.....

If we place "excess" charge on a conductor (excess meaning a charge not associated with the structure of the material itself) and then leave the conductor alone we will observe a net electric field inside the conductor of zero after a very short time period.

The "excess" charge will basically reside on the outside of the conductor and will distribute in such a way as to cancel any net electric field within the conductor. So a conductor that is in "electrostatic equilibrium" will have no net electric field inside the conductor.

Russ

physics wizard
guilcosa said:
I know an argument that i don´t like. It say´s:
If there were electric field inside a conductor in electrostaic equilibrium, it would excert force on the charges and move them.
But this argument implies that there are infinite charges inside the conductor. This is not very plausible, if charges have mass.
erg, its pretty easy to explain, i think later on ill send a picture of how it happens, but raughly, cuz i dont want to start use differentials, though i think its not too complex...
it only invovles calculating the dE, every dQ makes while referring to the geometric shape of the subject. though i do not know the general proof that would work for every unsimmetric subject(though i do know the gaus proof for it, but i dont like that much).

btw, did u know that newton already thought of what would happen to gravity in a hollow spere made of mass, kinda cool...

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Claude Bile
guilcosa said:
I know an argument that i don´t like. It say´s:
If there were electric field inside a conductor in electrostaic equilibrium, it would excert force on the charges and move them.
But this argument implies that there are infinite charges inside the conductor. This is not very plausible, if charges have mass.
Why do you think this implies that there must be infinite charges within the conductor?

Claude.

http://img170.imageshack.us/my.php?image=fieldspz6.jpg"

think of it a 2d view of a sphere...

the thing is that all the charges above the dot, are on the one hand closer to the dot, and on the other hand, there are less of them. and the charges below, have a bigger distance from the dot, but greater number.

but the full explanation will reqquier openning a book, reading lots of equasions in forums isnt much effective if u ask me... it takes patience

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for perfect conductor :
conductivity is considered infinity ( σ = infinity ) , but do u know what is conductivity ?
1-it is the ratio between conduction current density ( J ) and electric field ( E ) >> ( σ = J/E )
2-but again , what is the conduction current density ( J ) >> it is the charge density ( ρ ) times the average velocity of the charges in a conductor ( U ) ( J = ρ * U )
3- and the charge density ( ρ ) = number of electrons ( Ne ) times the electron charge ( e ) ( ρ = Ne * e )
4- and again , what is the average speed U ? >> it is the electron mobility ( u ) times the electric field ( E ) ( U = u*E )

so the laws are :
( σ = J/E ) & ( J = ρ*U ) & ( ρ = Ne*e ) & ( U = u*E )

then :
σ = J/E = ( ρ*U )/E = ( Ne*e*u*E ) / E
then:
σ = Ne*e*u
where sigma is the conductivity , e is the electron charge , u is the electron mobility , so returning to the question:

u said "this argument implies that there are infinite charges inside the conductor" , yes it implies that σ = Ne*e*u = infinity , or the number of electrons is infinity , this doesn't happen in reality , that's why it's called " perfect conductor " .

in reality we can approximate some materials to be perfect conductors because ( as lalbatros said ) they need huge E in order to "use" all the electrons in the material to cancel this E field.

if the conductor wasn't considered perfect , there sure must exist some E field inside it , but again this E field is negligible unless it was very huge .

( i wish to know what will happen if the E field was very strong , will the conductor be ionized or what will happen , i don't know)

=)

references:
1- the book: Fundamentals of applied electromagnetics ( by Dr. Fawwaz T. Ulaby )
2- wikipedia

rcgldr
Homework Helper
I had the impression that if a conductor was placed inside an external electrical field, like a metal plate placed between the charged plated of a capacitor, then an opposing field would be setup within the conductor, and the external and internal fields sum effect would be zero field within the conductor. However the conductor would have an internal field within it, it's just that that field would be equally opposed by the external field outside that conductor.

Born2bwire
Gold Member
I had the impression that if a conductor was placed inside an external electrical field, like a metal plate placed between the charged plated of a capacitor, then an opposing field would be setup within the conductor, and the external and internal fields sum effect would be zero field within the conductor. However the conductor would have an internal field within it, it's just that that field would be equally opposed by the external field outside that conductor.
Yeah, as long as we are dealing with statics you do not need a perfect conductor to have zero electric field on the interior.

But to note, this is a four year old thread...

Not to quote myself but....

There are many electric fields inside a conductor...the reason there is no "net" electric field is because the charges balance themselves in such a way to cancel the overall electric field.

As far as "electrostatic equilibrium" is concerned.....

If we place "excess" charge on a conductor (excess meaning a charge not associated with the structure of the material itself) and then leave the conductor alone we will observe a net electric field inside the conductor of zero after a very short time period.

The "excess" charge will basically reside on the outside of the conductor and will distribute in such a way as to cancel any net electric field within the conductor. So a conductor that is in "electrostatic equilibrium" will have no net electric field inside the conductor.

Russ

And yeah...this is a 4 year old thread....so maybe I shouldn't have posted again...

lol