# Electric Field in a Conductor

1. Feb 5, 2006

### Noesis

The electric field in a conductor goes to zero...or so my book says (which I'm inclined to believe).

But I don't really understand why.

I understand the polarization of the conductor in question, but how does this negate the electric field in the conductor?

The book says something about the electric field made by the polarized charges nullifies the electric field that is passing through....what if the conductor simply doesn't have enough electrons/protons to match the electric field in terms of charge?

If anybody could please clarify this a bit I would be most grateful.

2. Feb 5, 2006

### hellraiser

A conductor conducts. So the electrons are free to move. Now according to Coulomb's Law electrons will repel. This repulsion will cause them to move as far as away from each other as possible. If they are going to be far away as much as possible then the electrons must be on the outermost surface of the conductor. So there will be no net charge inside the conductor. Now according to Gauss Law enclosed charge in a conductor is zero so electric field is zero.

3. Feb 5, 2006

### Noesis

Thanks for the explanation man...but it still doesn't quite answer my question.

I know logically the electrons should move to the surface of the conductor in order to maximize their distance...but why when an electric field from another charge is passed through the conductor, does the conductor have zero electric field inside of it?

One side of the conductor turns negatively charged while the other side turns positively charged because of the absence of the electrons. Somehow this is supposed to cancel out the incoming electric field....and that's what I don't understand.

4. Feb 5, 2006

### spacetime

Suppose the electric field at a place is from left to right. Now when a conductor is put in the electric field, the electrons move to the left and hence there's a net negative charge on the left, and positive on the right. This creates a field which is from right to left, and hence opposite to the original field, and cancels it out inside the conductor.

And a conductor doesn't run out of electrons, it has many many of them, and ordinary electric fields aren't strong enough to make it run out of them.

spacetime
http://physics-help.blogspot.com" [Broken]

Last edited by a moderator: May 2, 2017
5. Feb 5, 2006

### Noesis

Thanks for the quick response.

Let me see if I got this straight now.

An electric field, either a positive or negative one, will strike a conductor. This will cause the polarization of the conductor in question, where the electrons will either be attracted or repelled by the field in question.

Since the conductor is polarized, one side of the conductor will be negatively charged whilst the other will be positively charged. The force produced by the field that caused the electrons to either be attracted or repelled will be proportional to the amount of electrons that have migrated. The stronger the force elicited the more electrons move.

Since the absence of electrons produces a positive charge, the positive charge produced by the absence of the electrons is equal in magnitude to the negative charge produced by the presence of electrons on the opposite side. Their fields are equal in magnitude but opposite in direction. It is almost like a massive dipole.

This causes an electric field inside the conductor. However since the electric field is equal in magnitude to the electric field striking it yet opposite in direction, the superposition of these two fields creates a net field of zero inside the conductor.

On the side opposite to where the electric field has struck, an equivalent electric field will be produced with the same magnitude and direction that is produced by either the negative or positive charge that exists there.

Now this creates a couple of questions for me:

-What if we had a really large electric field and a very small conductor, and we in fact ran out of electrons, would the electric field bleed through? I know this isn't probable as spacetime told me...but I am curious about it.

-What if a positive electric field strikes a conductor, that is not quite strong enough to cause the electrons on the other surface to migrate to it. Let's say it would just be strong enough move an electron if it were midway through the conductor...but obviously no electrons are present in the middle of the conductor.

Something like this could happen in a very wide/large conductor. Now this would mean that the electrons were indeed attracted to it, but no electrons from the other side transferred over. So there is no second electric field forming and thus no superposition of equal but opposite in direction electric fields. Would the electric field bleed through here as well or am I just thinking about something wrong?

-The electric field that comes out the other side of the conductor, is in essence not the same electric field that came in. The initial electric field has been negated and nullified. This new electric field does have the same magnitude and direction, but has a different source.

Does this in essence mean that we can transfer an electric field through a conductor, and not lose any of it's strength? If a conductor is 100 feet wide, we could have the same electric field at the very end of the conductor as we had at the beginning without losing any magnitude because of this phenomenon?

Thank you very much for your help guys, electric fields are pretty crazy.

6. Feb 6, 2006

### Noesis

Ah...I just realized a significant error in my thought process.

So my questions are pretty much null now.

Nevermind the above.

Electric fields are still crazy as I last said...but they've become just a bit more sane.

7. Sep 15, 2007

### kpk

---------- - ------------

Hi Noesis

Can you elaborate what is that error. coz I was thinking almost exactly like your previous message and was wondering whether it is correct or not.
Thanks
kpk

8. Sep 18, 2007

### kpk

I have a few questions:

1. Imagine there is a DC dry cell suspended from the roof a room by a non conducting thread.

An ordinary torch bulb is suspended from two flexible thin copper wires which are in turn suspended from the roof by a no. of non conducting threads.

The wires are connected to the terminals of the cell.

The copper wires are thin but has definite diameter.

The wires are suspended in widely separated condition till it reaches the terminals of the bulb.

Wires have its natural shape in suspended condition.

Question is : What is the direction of electric field which drives the current in the wires. –

(i) At the points where the wires are connected to cell terminals

(ii) at the bends of wires.

2. If the DC cell is replaced by an AC source of frequency 50Hz or so what is the instantaneous direction of electric field at the above points.

3. In the ac source case, will the conductors radiate? If radiates what is the direction and phase of the electro magnetic fields (around the conductors).

4. Suppose there are two metallic spheres one charged with +ve charges and other with negative charges (using Vande graf generator mechanism).

Let the spheres are widely separated so that the individual fields are negligibly small at the distance of the other sphere. – according to Coulomb's inverse square law)

Now let them be connected to each other by a flexible thin (but with definite diameter) conductor – suspended and is in natural shape –

Let there be a high resistance in the circuit so that the current is not very big and conduction will exist for quite some time.

Now all along the conductor, the field is strong enough to drive a current, irrespective of the large distance between the spheres.

(i) How this is made possible (field getting confined to the whole length of conductor and strong enough to drive currents at long distances).

(ii) What is the direction of electric field (which drives the current) inside the conductor at the point of connection between the sphere and conductor.

(iii) - do - at the bends of the conductor

(iv) Originally when there is no connecting conductor between the spheres, the fields would be distributed in the space in a symmetrical fashion and would be negligibly small after a considerable distance. But when the conductor wire is connected, the field becomes strong inside the region of space occupied by the conductor so that the influence of the field is extended to very large distance (i.e in the entire length of conductor) . Now in this case what is the direction and magnitude of field the space surrounding the spheres including the insides of conductor.

(v) What is the shape of Electric field due to a DC cell?

Thanks

9. May 12, 2011

### ADBisht

i have a question. if electric field inside a conductor become zero it means some free electrons are still in their position in the middle so how they are able to conduct electricity?

10. May 13, 2011

### ashishsinghal

Generally we take those materials as conductors which have a lot of free elecrons so that all of external field is nullified. The concept of dielectric will help you understand more about this.

11. May 18, 2011

### ADBisht

in a circuit (where current is continuously flowing ) external electric filed is also there ,so why there electric filed inside the conductor is never zero and current remain flowing(if electric field inside conductor had been zero flow of current would stop but this never happenend)why?????

12. May 18, 2011

### Andrew Mason

The field is the gradient of the potential:

E = dV/dx

The potential difference is V = IR. In a conductor with 0 resistance, V = 0, so dV/dx = 0. So the field in the conductor (the electric force per unit charge) must be 0. In other words, if there is no resistance, there is no force needed to move a charge through the conductor.

AM

13. May 20, 2011

### ADBisht

i am asking why electric field inside a conductor in a circuit is not zero??/while in electrostatics it is zero

14. May 20, 2011

### ADBisht

i am asking why electric field inside a conductor in a circuit is not zero ??/while in electrostatics it is zero

15. May 20, 2011

### Andrew Mason

Both are zero or very close to zero.

AM

16. May 26, 2011

### ADBisht

i think u r wrong if it is zero in a circuit current will not flow

17. Aug 25, 2011

### mejo.gejo

it will flow even if there is no net force (electric field). you can understand this if you adress for concept of force on right place, newton's laws- first one says that it is posible to have motion (uniformly rectilinearly) with zero net force. in electric that means if there is no resistance on the way, charge will flow but if we know that uniformly rectilinearly motion is equivalent to not moving, obviously if such current of charge run on some opstacle, it would not be able to over cross it.

if you look at wire (plain copper wire in e.g) you will see that there is all sorts resistance to flow of electrons; -1. atoms in the way, 2. repellinig force of electrons 3. by bending wire you get centripetal acceleration of electrons and if you do not have equivalent force electrons would in corners ( like cars) jump of the wire, and so on.

so ideally, flow of charge (current) without electric field (force) is posible if the right conditions are there.
lesser there is resistance, lesser are energy losses in wire and more energy is transffered in desired place/machine.

18. Sep 23, 2012

### yusufs

Hi.that also confuses me. why is it important ? what are the adventages of this?

19. Sep 23, 2012

### Andrew Mason

You are correct, if the conductor has some resistance. But if the conductor has negligible resistance, there is a negligible field. What do you think the field in a superconductor would be?

AM

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