# Measuring the net speed of an electron in a conductor

• simon.m

#### simon.m

Hello,
I have to start working on my physics extended essay and I got the idea of measuring the speed of an electron in a conductor. For instance, I could take a piece of wire (r) made from some conductor and I would like to find out the net speed of the electrons in the wire once I create an electric potential across the conductor.
My only idea (so far) to do this is to build a simple DC electro-motor (or something on that principle) on which I would be able to measure the torque applied on the coil and from that I could calculate the speed. However, I can see a lot of sources of uncertainties in this experiment.
So my question is: If you know (or can think) of any feasible(!) experiment that enables measuring the net speed (or velocity -- that's the easy part :) of an electron in a conductor (a piece of wire), could you please write your thoughts, comments and suggestions? Please respond even if you know about someone who has tried the experiment I described and provide an URL or other contact to the person.
Thank you very much.
Simon

simon.m said:
Hello,
I have to start working on my physics extended essay and I got the idea of measuring the speed of an electron in a conductor. For instance, I could take a piece of wire (r) made from some conductor and I would like to find out the net speed of the electrons in the wire once I create an electric potential across the conductor.
My only idea (so far) to do this is to build a simple DC electro-motor (or something on that principle) on which I would be able to measure the torque applied on the coil and from that I could calculate the speed. However, I can see a lot of sources of uncertainties in this experiment.
So my question is: If you know (or can think) of any feasible(!) experiment that enables measuring the net speed (or velocity -- that's the easy part :) of an electron in a conductor (a piece of wire), could you please write your thoughts, comments and suggestions? Please respond even if you know about someone who has tried the experiment I described and provide an URL or other contact to the person.
Thank you very much.
Simon

Er.. I think you are going to set yourself up for a failure.

When you apply a potential difference across a wire, the "current" that you detect is not due to the electron that entered at one end and exit the other. It is not the same electron that came out. In fact, you can't tell which electron is which once it is inside a conductor. This makes determining the "speed of an electron in a conductor" a rather meaningless quantity.

While there are average speed of the conduction electrons being cited, these are based on the statistics of a free electron gas and the plasma velocity of the whole group of electrons. Most of the time, these are based on indirect inference based on statistics. Others more complicated form require the knowledge of the self-energy interaction. I don't think you want these.

Zz.

ZapperZ,

But if he could estimate the concentration of conduction electrons, then he could get their average speed along the direction of the current. Right?

Sorry, I am probably missing something... if you shoot a particle (e-) through a magnetic field, the force on the particle (that makes it turn) is related to the initial velocity of the particle, am I wrong?
Here I am just making the stream of the electrons directed in one direction and the turn of all the elctrons is done by the spin of the coil.

simon.m said:
Sorry, I am probably missing something... if you shoot a particle (e-) through a magnetic field, the force on the particle (that makes it turn) is related to the initial velocity of the particle, am I wrong?
Here I am just making the stream of the electrons directed in one direction and the turn of all the elctrons is done by the spin of the coil.

But this is NOT the same as measuring the speed of electrons in a CONDUCTOR, which is what you were intending to do. Electrons in a conductor behave in a different way than free electrons in vacuum.

Think about it this way. You have a U-tube filled with water. If you force more water down one arm of the U, there will be water being spilled at the other end of the U. Is the water that came out the same as the water than you poured in? And to add to the complication, you only notice the BULK volume of water that went in. You have no clue how the individual water molecule behaved. Based on this, are you able to deduce the "speed" of the water molecule when you do this experiment?

jdavel said:
But if he could estimate the concentration of conduction electrons, then he could get their average speed along the direction of the current. Right?

There is an average GROUP velocity, yes. That's what I meant earlier. But the individual velocity of ONE electron, even using the classical Drude model, is random and very much like a Brownian motion. However, this velocity cannot be deduced from measuring the "transit" time between between the switching on of the potential and current detection at the other end.

Zz.

ZapperZ:
thank you for your answer, I think that I understand your point and you are right about the fact that individual electrons move very much like in a Brownian motion. however, in the case of a motor, it is the velocity of the particles in the direction of the current that matters. I probably did not make myself clear initially because I realize that I cannot measure the instantaneous velocity of an individual particle.
But do you think I can measure the time in which an electron overcomes a distance L of the wire? (I realize I made a mistake calling this the speed of electrons in a conductor)
Thanks,
Simon

simon,

Right, so if you had one electron, you could find out how fast its going. But you have a lot of electrons, and each one has a little force exerted on it by the magnetic field. So the total force you measure will be proportional to the number of electrons AND their velocity, N*v. Without N how can you tell if the force is from a lot of electrons going slow or from just a few going fast? I don't think you can.

ZapperZ,

You're certainly right that the random motion can't be found with the method simon is describing. But I've been assuming that what he means by "net speed" of electrons when a voltage is applied is the drift velocity. His last post seems to confirm this, I think.

simon.m said:
ZapperZ:
thank you for your answer, I think that I understand your point and you are right about the fact that individual electrons move very much like in a Brownian motion. however, in the case of a motor, it is the velocity of the particles in the direction of the current that matters. I probably did not make myself clear initially because I realize that I cannot measure the instantaneous velocity of an individual particle.
But do you think I can measure the time in which an electron overcomes a distance L of the wire? (I realize I made a mistake calling this the speed of electrons in a conductor)
Thanks,
Simon

How do you propose to do this?

What you have in a motor is nothing more than the effect of current flowing in a wire. Now while it is true that current is defined as the amount of charge going through a crossectional area of the wire per unit time, this is the MACROSCOPIC definition of current. At the microscopic level, even within the classical picture, you have electrons bouncing around at random, either due to collision with the massive ions, or with themselves. At best, all you can deduce is the average group velocity of the whole glob.

Thus, if you equate the current value as the velocity of individual electrons, you'll get the wrong answer.

Zz.

jdavel said:
ZapperZ,

You're certainly right that the random motion can't be found with the method simon is describing. But I've been assuming that what he means by "net speed" of electrons when a voltage is applied is the drift velocity. His last post seems to confirm this, I think.

Ah, but here's the "paradox". If you take the typical drift velocity (which is really a time-averaged velocity), you'll never be able to explain the almost instantaneous flow of current in a conductor. Try it. Have a long wire, for example (100 m will do), and figure out how long it'll take for a light bulb to turn on the moment one applies a potential difference using the drift velocity. You'll find that your calculation difference considerably when compared to what actually happens.

Moral of the story: can you use what he's proposing to actually measure the drift velocity, if this is the quantity that is intended to be measured?

Zz.

simon.m said:
however, in the case of a motor, it is the velocity of the particles in the direction of the current that matters.

I forgot to comment on this. If you are going to use a "motor" as an example on how to measure this, we then arrive at a possibly amusing answer. Doesn't an electric motor typically works using AC current (maybe with a rectifier?)? If so, then the average velocity of the electrons in the conductor is.... whoa... ZERO! :)

Zz.

You have probably seen a DC motor with a commutator. Nevertheless, my point is not to buil a motor but rather to measure a force applied at a certain moment on a piece of wire of length L with a current I running through it.

Zapper,

No, you certainly can't find drift velocity by seeing how long it takes for a light to go on after throwing the switch.

But if you know the concentration (per unit vol) of conduction electrons, and the current, and the dimensions of the wire, then you can find the drift velocity. Right?

But simon, I don't think the way you're using the magnetic field will help you get at the drift velocity. There is a method based on the Hall effect that uses a magnetic field perpendicular to the current direction that's used to get at these values. But it takes some special equipment and a very thin sheet of conducting material to get useful results. You might look it up though and learn about it. It's a clever experiment, and in semiconductors (like doped silicon) it gives some very surprising results!

simon.m said:
You have probably seen a DC motor with a commutator. Nevertheless, my point is not to buil a motor but rather to measure a force applied at a certain moment on a piece of wire of length L with a current I running through it.

Then all you're doing is measuring the magnetic force due to current flow. What does this have anything to do with "electron velocity in a conductor"?

Zz.

I would measure the force and from that find (calculate!) the <u> net </u> speed of an electron (or the average speed of the stream of electrons) in the wire.

simon.m said:
I would measure the force and from that find (calculate!) the <u> net </u> speed of an electron (or the average speed of the stream of electrons) in the wire.

How do you go from the magnetic "force" to "speed of an electron"?

Zz.

A magnetic force in a wire with current I and length l in a field of strength B is: F=BIl
Product Il is the same as qv where q is the total electronic charge of the carriers in this length l and v its velocity. So if we are using copper wire we should indeed be able to work out (by measuring F while the rotor is at standstill) the additional speed of the electrons in the direction of and caused by the applied potential difference. This particular v of electrons in copper wire cannot go much higher then 1mm/sec otherwise the wire would melt.

The fast responce of light in say switching electric light is caused by the electric field which is established when the circuit is made. This speed is 1/3C where
C is speed of light in vacuum.

Last edited:
erickalle said:
A magnetic force in a wire with current I and length l in a field of strength B is: F=BIl
Product Il is the same as qv where q is the total electronic charge of the carriers in this length l and v its velocity. So if we are using copper wire we should indeed be able to work out (by measuring F while the rotor is at standstill) the additional speed of the electrons in the direction of and caused by the applied potential difference. This particular v of electrons in copper wire cannot go much higher then 1mm/sec otherwise the wire would melt.

The fast responce of light in say switching electric light is caused by the electric field which is established when the circuit is made. This speed is 1/3C where
C is speed of light in vacuum.

.. and again, it appears as if all the previous discussion on the meaning of "current" and "drift velocity" in a conductor in this thread appears to just have fallen on deaf ears. It's as if it never happened.

Zz.

ZapperZ,

What are you getting at here? Are you suggesting one cannot measure the drift velocity in a conductor?

- Warren

chroot said:
ZapperZ,

What are you getting at here? Are you suggesting one cannot measure the drift velocity in a conductor?

- Warren

Nope, that's not what I'm suggesting. The current value that is being measured can be related to the drift velocity. I think this has been established somewhere in this thread. However, this "v" that is associated with the current, and given the term "drift velocity" cannot be confused with the vacuum electron situation, in which there REALLY is a conglomerate of velocity without an individual electron in a brownian motion. The vacuum case is very different than a conduction electron case, and this is just at the simplest level here.

If I were advising someone about this project, I'd rather tell them to just write down the current and be done with. This is more transparent than trying to explain how such a thing relates to a "velocity" of an electron (would someone at this level understand "drift velocity"?), not to mention the confusing aspect of having a constant value of a velocity when there is a net electrostatic force being applied across the conductor.

Zz.