## Electron flow in a wire

Hi friends!!! I know this is a question many people might have posted on the forum. I saw many threads but still have some doubt in my mind, about why do electrons flow in a wire when we attach a battery to it. Being more specific, my doubts are as follows :-
(1) My book says that an electron will emerge with an acceleration a = -eE/m. How come it emerges with uniform acceleration when electric field is applied. That too when it suffers collisions and moves under random motion, i.e. how can we be so decisive about it's acceleration? Then they have applied formula for uniform acceleration : v = u + at.
(2) How come the electric field in the wire is uniform throughout?
(3) I also need some detail about the random motion of the electrons before and after the field is applied, i.e. the path when the flow of the electrons is biased in one direction.

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 Quote by Ashu2912 (1) My book says that an electron will emerge with an acceleration a = -eE/m. How come it emerges with uniform acceleration when electric field is applied. That too when it suffers collisions and moves under random motion, i.e. how can we be so decisive about it's acceleration? Then they have applied formula for uniform acceleration : v = u + at.
In between collisions, the only force on the electrons is that of the electric field. Note that they are talking about the component of the velocity in the direction of the field.
 (2) How come the electric field in the wire is uniform throughout?
The current must be the same throughout the wire, otherwise charges will build up until the current is the same. Since the wire is uniform, there is a fixed relationship between current and field throughout the wire.
 (3) I also need some detail about the random motion of the electrons before and after the field is applied, i.e. the path when the flow of the electrons is biased in one direction.
With no field applied, the electrons exhibit random thermal motion. When the field is applied, it exerts a force in the direction of the wire. Thus an acceleration is imposed on top of the random motion, which ends up giving the electrons a drift velocity along the wire.

 I thought in conducting wire, velocity $u_e = \mu_e \vec E$. Where $\vec E$ is develope due to voltage drop across the wire. The better the conductivity, the slower the velocity because the $\vec E$ is smaller.

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## Electron flow in a wire

That's the average velocity. Individual electrons, however, constantly accelerated due to electric field, and loose their velocity whenever they "collide" with the lattice. Naturally, it's all a whole lot more complicated due to quantum mechanics, but this simple model lets you predict a lot of properties of the conductor.

 Quote by Doc Al The current must be the same throughout the wire, otherwise charges will build up until the current is the same. Since the wire is uniform, there is a fixed relationship between current and field throughout the wire.
Can you please explain it in a better way because I didn't understand this?

 Quote by Doc Al In between collisions, the only force on the electrons is that of the electric field. Note that they are talking about the component of the velocity in the direction of the field. With no field applied, the electrons exhibit random thermal motion. When the field is applied, it exerts a force in the direction of the wire. Thus an acceleration is imposed on top of the random motion, which ends up giving the electrons a drift velocity along the wire.
Do you mean the acceleration in the direction of the field? However, since the electrons move in random motion even when the field is applied, don't you think that we must analyse their motion in multiple dimensions? Does the force from the nuclei and other electrons get cancelled as in the static situation? But then why do the move randomly even if the electric field, and thus force on them is in one direction?

 what book are you using??

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 Quote by Ashu2912 Do you mean the acceleration in the direction of the field? However, since the electrons move in random motion even when the field is applied, don't you think that we must analyse their motion in multiple dimensions? Does the force from the nuclei and other electrons get cancelled as in the static situation? But then why do the move randomly even if the electric field, and thus force on them is in one direction?
Maybe if I give you a "catch name", you might be able to look it up. Search for The Drude Model, or open a solid state physics text such as Kittel or Ashcroft/Mermin. The Drude model will give you a treatment of electron transport in metals by using the free-electron gas approximation. It is a purely classical treatment using the standard Maxwell-Boltzmann statistics.

Zz.

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 Quote by Ashu2912 Can you please explain it in a better way because I didn't understand this?
I made several statements. Which are you referring to? The key is that the current must be the same throughout the wire, else charges will build up and throttle the current flow.

 Quote by Ashu2912 Do you mean the acceleration in the direction of the field?
Yes.
 However, since the electrons move in random motion even when the field is applied, don't you think that we must analyse their motion in multiple dimensions?
Not really, at least to draw some crude conclusions. (The model used by your book--I assume--is a simplified version of the Drude model mentioned by ZapperZ. And that model is itself only a classical approximation to a fuller treatment. But it's good enough. What book are you using, by the way?)
 Does the force from the nuclei and other electrons get cancelled as in the static situation?
I think you're asking if the inside of the wire is electrically neutral. Yes.
 But then why do the move randomly even if the electric field, and thus force on them is in one direction?
There is a relatively high speed random thermal motion of electrons in the wire. With no field, the average velocity of the electrons is zero. (Not net motion along the wire.) When you impose an electric field, the electrons are accelerated in the direction of the wire (in between collisions with the lattice), so there is now a net motion of the electrons. This is the 'drift velocity'.

Picture it this way. With no field, the electrons move in straight lines in all directions (in between collisions with the lattice). With a field, those straight lines are now parabolic paths (much like a projectile in a gravitational field), with a net displacement in the direction of the force on them.

 I am using the NCERT textbook (CBSE textbook in India) for Class 12th.

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 Quote by Ashu2912 I am using the NCERT textbook (CBSE textbook in India) for Class 12th.
OK. I'm not familiar with that particular text.

I am a student studying in Grade 12 in India under the CBSE board and use the NCERT textbook prescribed by the board. Indeed, the book explains the phenomenon on the basis on the basis of the Kinetic theory of gases (Boltzmann and Maxwell). Thanks for your valuable replies.

 Quote by Doc Al I think you're asking if the inside of the wire is electrically neutral. Yes.
Here, I am referring to the electric field (and thus electrostatic force) of the nuclei and other free electrons on an electron under consideration!!!

 Will Fundamentals of Physics by Resnick, Halliday and Walker do good?

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 Quote by Ashu2912 Here, I am referring to the electric field (and thus electrostatic force) of the nuclei and other free electrons on an electron under consideration!!!
So am I. I'd say that except during a collision, there's no electric field to worry about due to the charged particles within the wire. It's electrically neutral.

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 Quote by Ashu2912 Will Fundamentals of Physics by Resnick, Halliday and Walker do good?
I used (many years ago) the original version and thought it was pretty good. So perhaps the current version is good as well.

 Haliday and Resnick are the best physics teachers. They made me love physics.

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 Quote by Ashu2912 I am a student studying in Grade 12 in India under the CBSE board and use the NCERT textbook prescribed by the board. Indeed, the book explains the phenomenon on the basis on the basis of the Kinetic theory of gases (Boltzmann and Maxwell). Thanks for your valuable replies. Here, I am referring to the electric field (and thus electrostatic force) of the nuclei and other free electrons on an electron under consideration!!!
Here is a common problem that I see in many posts, and it should be clarified once again.

In a conductor, numerous atoms have come together to form this solid. When that occurs, the individual properties of the atoms no longer dominates. Rather, the collective properties of these many atoms now take over, at least, for many of the common properties of solids that we encounter. For example, a copper atom does not "conduct", but a copper metal does!

When many of these atoms combine to form a conductor, there are bands of states called the conduction band. In this band, there is a sea of conduction electrons that are free (or pseudo-free) to move. Here, depending on what approximation that you make, these electrons are truly free, meaning they do not see the nucleus potential at all. This is the Drude model of conduction electrons where the electron form a free particle gas. The Bloch model, on the other hand, will have some periodic potential to represent the location of the ions in a crystal lattice.

The moral of the story here is that, once we have a conductor, and once you ask about motion of electrons in a conductor, you need to stop thinking about "atoms". Rather, the conductor how has its own set of properties, and the conduction electrons are governed by those properties.

Zz.