# Why an electron's drift velocity is so slow?

Electrons are moving VERY fast. However, they don't have a high drift velocity in a circuit. Why? Is it because every time they advance a little bit they collide with an atom? Or is it because the electric field in a circuit is not strong enough so the electrons don't get pushed enough?

ZapperZ
Staff Emeritus
Electrons are moving VERY fast. However, they don't have a high drift velocity in a circuit. Why? Is it because every time they advance a little bit they collide with an atom? Or is it because the electric field in a circuit is not strong enough so the electrons don't get pushed enough?

It is the same reason the wind speed is considerably slower than the speed of air molecules. There is a lot of collisions going on with each other.

Zz.

tech99
Gold Member
Electrons are moving VERY fast. However, they don't have a high drift velocity in a circuit. Why? Is it because every time they advance a little bit they collide with an atom? Or is it because the electric field in a circuit is not strong enough so the electrons don't get pushed enough?
It is because the current in a circuit is equal to Charge x Velocity. The charge of the electrons in a few cm of copper wire is very large. For instance, it is similar to the total charge of a D-cell. In order to convey a current, they have only to move very slowly indeed.
Not only that, due to the huge charge and the very strong static field from the electrons, the slightest acceleration, for instance by switching on, creates EM radiation very easily.

ORF and vanhees71
Staff Emeritus
Gigie, slow relative to what? What do you think their speed should be?

ZapperZ
Staff Emeritus
It is because the current in a circuit is equal to Charge x Velocity. The charge of the electrons in a few cm of copper wire is very large. For instance, it is similar to the total charge of a D-cell. In order to convey a current, they have only to move very slowly indeed.

I think there's a problem with cause-and-effect here. It seems that you've used the effect and turned it into the cause.

I can have the same amount of charge, and put it in, say, a vacuum and apply the same potential difference. There's nothing there now to prevent the electrons from moving very fast, much faster than the drift velocity, and thus, giving a larger current. The charges are not compelled to "convey" a current, or a certain amount of current.

Instead, it is the resistivity that puts a value on the current for a given potential difference. This is clearly shown in the Drude model where the scattering rate and the mean free path directly affect the resistivity and the drift velocity.

BTW, your reference to the "total charge of a D-cell" is incorrect. A battery does not store charge.

Zz.

tech99
Gold Member
Well I suppose as our starting point we could have defined a circuit in which 1 Amp was flowing. Then we could calculate the velocity quite easily.
I agree that strictly speaking a battery does not store charge - but it would be pedantic to have specified a 10F capacitor. I was trying to make the point that the electronic charge in a copper wire is very large, more than one might expect. This appreciation, to my mind, makes for an easier visualisation of conduction and also of EM radiation.

ZapperZ
Staff Emeritus
Well I suppose as our starting point we could have defined a circuit in which 1 Amp was flowing. Then we could calculate the velocity quite easily.

But I still do not see what this has anything to do with why the drift velocity is considerably smaller than the electron speed. Again, if this were done in vacuum (and trust me, *I* do this in vacuum in a particle accelerator), the charge, how ever large it is, will have a large speed!

The current here is the outcome. You already have a specific charge density, and you're applying a fixed potential difference. Those are your starting parameters, not the current. You don't get to choose the current, because I can easily change the wire to another conductor with a different resistivity, resulting in a different current using the same values of the starting parameters. Your explanation doesn't explain the origin of the wildly different values in the drift velocity and electron speeds.

I agree that strictly speaking a battery does not store charge - but it would be pedantic to have specified a 10F capacitor. I was trying to make the point that the electronic charge in a copper wire is very large, more than one might expect. This appreciation, to my mind, makes for an easier visualisation of conduction and also of EM radiation.

I still don't see the connection here and why this is even relevant.

Zz.

Well I suppose as our starting point we could have defined a circuit in which 1 Amp was flowing. Then we could calculate the velocity quite easily.
I agree that strictly speaking a battery does not store charge - but it would be pedantic to have specified a 10F capacitor. I was trying to make the point that the electronic charge in a copper wire is very large, more than one might expect. This appreciation, to my mind, makes for an easier visualisation of conduction and also of EM radiation.
The electronic charge in a length of metal wire is easily calculated !! What do you mean by 'more than one might expect'....

Gigie, slow relative to what? What do you think their speed should be?
I did a google search that explain that the speed of an electrons, if it is not disturbed by anything, is about 2,200 kilometers per second. However the length the electrons travel in an electric circuit is different.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
I did a google search that explain that the speed of an electrons, if it is not disturbed by anything, is about 2,200 kilometers per second. However the length the electrons travel in an electric circuit is different.
Taken out of context, this is a nonsense figure. There is no given "speed of an electron" - it depends on what you do to your electrons and relative to what you measure. Please provide references to such statements.

ZapperZ
Staff Emeritus
Taken out of context, this is a nonsense figure. There is no given "speed of an electron" - it depends on what you do to your electrons and relative to what you measure. Please provide references to such statements.

This is roughly the Fermi velocity of metals. It is a usual "reference" speed of the electrons in an electron gas.

http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/fermi.html

Zz.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
This is roughly the Fermi velocity of metals. It is a usual "reference" speed of the electrons in an electron gas.

http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/fermi.html

Zz.
Well, yes, but the point is that I should not have to know that in order to understand what he is talking about. He could have dug up a figure from anywhere. It is also not the case any electron "usually" move at that speed (unless it is in an electron gas of appropriate temperature - which is the context) which seems to be the impression of the OP (I may be wrong of course, but it is how I read it).

Staff Emeritus
Yes, but at least now we are zeroing in on the misunderstanding - that there is some speed that electrons, unlike, say baseballs, "should" be traveling at.

vanhees71
Gold Member
Well, it depends a bit on the model you are considering. If you take the Drude-Sommerfeld model (i.e., the Drude model of the conduction electrons in a metal as an ideal gas together with Sommerfeld's use of the Fermi statistics) then of course the electron velocity consists of the collective flow ("macroscopic velocity" or "drift velocity") of the conduction electrons, making up the macroscopic current density ##\vec{j}##, which also enters the consitutive law (local form of Ohm's law), ##\vec{j}=\sigma \vec{E}## (usual non-relativistic limit, neglecting the magnetic field), and the "thermal fluctuations" around this collective-flow velocity, whose magnitude usually is much higher than the drift velocity but undirected, i.e., in the local rest frame of the fluid it averages out to 0.

Staff Emeritus
This is an I-level thread, and should probably really be a B. The OP is not starting with the Drude-Sommerfeld model.

vanhees71
Gold Member
Well, the Drude-Sommerfeld model is definitely I level, and at this point of the debate, where statistical theory has been invoked, you have to discuss it at least at this level!

ZapperZ
Staff Emeritus
The OP actually had an inkling of a possible mechanism right in the very first post:

Is it because every time they advance a little bit they collide with an atom?

It just needs to be refined since the collision here is more than just with the atom. Unfortunately, it didn't help that tech99 gave a rather odd response, and that was more problematic than what the OP has posted.

Zz.

vanhees71
Gold Member
Well, the most simple approach here is indeed just the Drude model. You start thinking about a conduction electron, which moves through the wire, driven by the applied constant electric field ##E## (in direction of the wire). This electron is free exept for collisions with all kinds of stuff like impurities in the crystal lattice, lattice vibrations "phonons" etc. etc. We don't care for this but just assume that there's a friction force propotional to its velocity, ##F=-\alpha m v##. Thus the equation of motion of this electron reads
$$m \dot{v}=q E-\alpha m v.$$
What happens is that in the beginning when the electric field is switched on the electron accelerates and after a relatively short time reaches a velocity, where the friction just compensates for the electric force, and then you get a constant velocity, the drift velocity. That gives, because then ##\dot{v}=0##,
$$v=\frac{q E}{\alpha m}.$$
Now the total current density is given by ##j=n q v##, and thus you get Drude's formula
$$j=\frac{n q^2 E}{\alpha m}=\sigma E,$$
and thus for the electric conductivity
$$\sigma=\frac{n q^2}{\alpha m}.$$
For the drift velocity you thus find
$$v=\frac{j}{q n}=\frac{I}{A q n},$$
where ##A## is the cross section of the wire. For a realistic estimate for household current, see
https://en.wikipedia.org/wiki/Drift_velocity#Numerical_example
As you see, you get a tiny drift velocity of ##v \simeq 2 \cdot 10^{-5} \text{m}/\text{s}##. The smallness if of course indeed due to the huge amount of conduction electrons in the wire, i.e., because the number density of counduction electrons ##n## is a large number.

In the final sentence of this paragraph at Wikipedia concerning the Fermi velocity they should rather talk about Fermi speed, i.e., the magnitude of this velocity. The reason is what I told already in my previous posting: The electrons' thermal motion (i.e., in this case their Fermi motion) is random, i.e., it averages out to 0 when averaging over quite small volumes and/or times.

ORF and Delta2
If you look at any 1 electron it is almost as likely to be going up-stream (against the applied voltage) as it is to be going down-stream. The next question could be "why does an electron ever go against the applied voltage?" My answer would be that on a scale that small, random interactions with individual nuclei and other electrons are the dominant forces causing individual electrons to accelerate and move. Any applied voltage is extremely minuscule compared to all of the other, more local interactions. Every once in a while, an electron may be almost perfectly balanced between all the other forces around it and move in the direction of applied voltage, but that situation is relatively rare and short-lived.