Electric Current: Explained with Fields

[arun_mid]

What is electric current?
Let me explain my idea of it with an example of a long wire connected to the two terminals of a battery. The battery applies an electric field to the surrounding, causing a shift in the position of the electrons of the wire, especially the ones nearby. The speed and number of electrons that shift depend on the material. The shift of these nearby electrons causes change in the electric field distribution, so more electrons nearby shift, causing further change, and so on, like a stack of dominoes. This change in electric fields takes place at the speed of light. So the current is said to move at the speed of light, although the electrons take quite some time (compared to c anyway) to shift even an infinitesimal distance.
Is this right?
If not, please try to explain current using fields rather than 'pd causes current' stuff. I agree that it does but it would be a lot clearer to me if fields were used to explain it. I'm sure there isn't much difference.

 

[Tide]

Actually, I've never heard anyone say the current moves at the speed of light with respect to electrical circuits of the kind you describe.

The electrical current density can be expressed as

$$\vec j = -n_e e \vec v_d$$

where $n_e$ is the electron number density (usually very large!), e is the elemental charge and $\vec v_d$ is the electron drift velocity (usually very small!).

Generally, Ohm's Law (in isotropic media) relates the current density to the electric field as

$$\vec j = \sigma \vec E$$

where $\sigma$ is the electrical conductivity and $\vec E$ is the electric field.

The reason electrons don't "instantaneously" move all the way around the circuit is that their directed motion is very quickly randomized by their (very) frequent collisions with ions (aka Joule heating).

 

[arun_mid]

but since the electrons move slowly, why does the circuit work so quickly? Exactly what goes on? Is it simply because they START to move that the circuit works?

 

[inha]

well kind of yes. the electric field propagates much faster than the electrons.

 

[Tide]

but since the electrons move slowly, why does the circuit work so quickly? Exactly what goes on? Is it simply because they START to move that the circuit works?

If the electric field is turned on "instantaneously" then the electrons respond according to

$$v = \frac {\sigma E}{n_e e} \left( 1 - e^ {-\frac {n_e e^2}{m_e \sigma} t \right)$$

so it does take some time for the electrons to reach their "terminal velocity." However, for typical conductors, the exponential tends to zero very quickly.

 

[Renge Ishyo]

My feeble understanding of electric current:

Using a metal for simplicity, within a body where electrons are free to interact with each other, Electrons flow from regions of where there are large numbers of electrons to where there are less. Since electrons repel other electrons with a force, you can think of it as the force on one side of an electron (the side nearest the large number of electrons) being greater than the force on the other side of the electron (nearest the smaller number of electrons, which are still repulsing but not as strongly as on the other side). Hence a net force will spread the electrons evenly across a metal surface until the force on both sides of the electron are the same.

To intensity the effect, you can remove electrons from one side of a metal, and dump more electrons on the other side (in reality, you separate two ends with different electron concentrations and connect them with a wire as the pathway for the electrons to flow). Thus, the movement of the electrons will always be towards the positive side that the electrons are attracted to and away from the negative side that is repulsing the electrons and pushing them towards the same direction. The electric current in this view can be seen as the net force being applied to the electrons that it is *pushing them towards their ultimate destination*, the positive terminal. Note that, just like if you started pushing a car that wouldn't start to a gas station 10 miles up the road, you don't arrive at your destination instantaneously...even if you start pushing constantly (so that the force moving the car forward is always constant) there is a time delay between the time you start pushing and the time when the car finally arrives and you can stop pushing. Think of the electric current as the constant force pushing the electrons towards their destination. Strong currents push those electrons to their destinations very fast while weak currents get them there slowly (just like pushing the car faster will get your car to that gas station faster than pushing it there slowly). Either way it still takes time for the current to push the charges from point A to point B. If the transfer of electrons was instantaneous we wouldn't even be able to detect a current (because the current stops when the charge distribution is finally even).

There. Now we just have to wait for someone who know's what he's talking about to rip my explanation to bits

 

[arun_mid]

actually your explanation makes sense, except that i said that an electric field from the positive terminal pulls the electrons, and the electrons follow, like a chain. you say that repulsion from the negative terminal causes them to flow.
I can understand the initial 'flow' of electrons. what i don't understand is why, for instance, a light bulb lights within 1 second (maybe much less) while the drift velocity of an electron is so slow. I explain this by saying that a simple shift in electrons near the positive terminal causes a change in electric field configuration. that causes more electrons to move, and so on, in a chain reaction, at a much faster rate than the rate at which the electrons move.
maybe I was totally wrong about the speed of light thing. but drift velocity is very slow.

 

[Renge Ishyo]

Well, yes...certainly your analogy is more consistent with the convention of electric current starting from the positive terminal.

In reality, there are electrons all throughout the metal (we talk of them being in separate places to simplify the situation), so when some at "one side" move, ALL the electrons are moving along the line instantaneously to accommodate the excess electrons moving in from behind. The movement of all the electrons doesn't *stop* until the charge distribution throughout the material is even, which takes awhile, but the collisions between electrons take place almost immediately as I understand. Dominos is close, but the problem with that analogy is that the dominos at the end don't move until they are "touched" by a falling domino behind them. Instead imagine beads on a string that are closely pressed against each other along the length of the string so that if you moved one bead it would push against ALL the beads on the other side of it out all the way down the string.

This is an imperfect analogy too, but just keep in mind that the electric current is motivated by two forces at all times, electric attraction by the positive end and electric repulsion at the negative end. The electrons are all moving down the line by these forces like beads in order to accommodate the excess beads stacked up on the string on one end.

That's the best I can do with my limited knowledge of physics. The drift velocity seems like an unrelated idea that has more to do with how fast the charge is traveling per unit time (the strength of the force pushing the two sides together determining how fast ultimately). Or in other words, it refers to the magnitude of the current only. You can have strong currents caused by a large difference in charge between the ends (a large force) that move lots of charge over a distance per second (large drift velocity) or weak currents moving less charge over a distance per second (smaller drift velocity) with a smaller potential difference between the ends. The drift velocity, and I sure hope I remember this correctly, is the *rate* at which the current is moving. However, the electric current just describes *how* charge moves, and it can move at many different rates depending on the size of the difference in charge between the positive and negative ends.

So long as none of this is incorrect, I think that'll be my last stab at trying to explain it (before I end up totally wrong about something)

 

[Tide]

arun,

what i don't understand is why, for instance, a light bulb lights within 1 second (maybe much less) while the drift velocity of an electron is so slow.

I believe I already explained this. Let me try it this way:

When the switch is turned on the electrons along the full length of the wire are immediately subjected to the applied electric field and their motion is subject to Newton's laws of motion, i.e. force = mass x acceleration. All of the electrons are accelerated by the applied field. While they are being accelerated, the electrons collide with ions in the wire. That tends to slow the electrons down.

After some time, the slowing down effect on the electrons due to collisions with the ions balances the speeding up effect of the electric field. When that state is reached, the electrons move at what is called their drift velocity.

As I already pointed out to you, this condition occurs very quickly for typical wires. You must realize that in a good conductor, the number of electrons in even a tiny volume is VERY large! A length of wire 1 cm long might contain $10^23$ electrons, give or take. That is a LOT! So even with a very small drift velocity a wire can carry a lot of current simply because there are so MANY electrons.

Of course, this includes the electrons in the filament as well. They are subjected to the same applied electric field when the switch is turned on. It is not like the electrons from the electrical generator down at the river have to travel all the way to the filament in order for electrons in the filament to start moving. Once the switch is turned on, the electric field makes its presence known to all of the electrons in the circuit essentially at the speed of light. It takes only a few nanoseconds for the electric field to affect the electrons in the filament after you turn on the switch.

 

[ZapperZ]

This question has had several incarnations. You may want to check this thread, for example.

https://www.physicsforums.com/showthread.php?t=79645&highlight=speed+current

Zz.

 

[El Hombre Invisible]

but since the electrons move slowly, why does the circuit work so quickly? Exactly what goes on? Is it simply because they START to move that the circuit works?

Current is the flow of net positive charge, not actual particles in the wire. Each moving electron exerts a repulsive force on the next electron it is moving towards, which exerts a force on the one in front of it, and so on and so forth. It also causes a decrease in repulsion (in the opposite direction) in the electron behind it, which in turn is pushed in the same direction by the electron behind it, and so on and so forth. Because of this, electron flow at one end of a wire can cause electron flow at the other (or flow in the middle causes flow at both ends) at a faster rate than can be explained by the speeds of the electrons themselves. Otherwise there would be quite some delay when turning on a light.

 

[arun_mid]

Thanks for all your explanations. I think I understand now.

 

[roger]

arun,



I believe I already explained this. Let me try it this way:

When the switch is turned on the electrons along the full length of the wire are immediately subjected to the applied electric field and their motion is subject to Newton's laws of motion, i.e. force = mass x acceleration. All of the electrons are accelerated by the applied field. While they are being accelerated, the electrons collide with ions in the wire. That tends to slow the electrons down.

After some time, the slowing down effect on the electrons due to collisions with the ions balances the speeding up effect of the electric field. When that state is reached, the electrons move at what is called their drift velocity.

As I already pointed out to you, this condition occurs very quickly for typical wires. You must realize that in a good conductor, the number of electrons in even a tiny volume is VERY large! A length of wire 1 cm long might contain $10^23$ electrons, give or take. That is a LOT! So even with a very small drift velocity a wire can carry a lot of current simply because there are so MANY electrons.

Of course, this includes the electrons in the filament as well. They are subjected to the same applied electric field when the switch is turned on. It is not like the electrons from the electrical generator down at the river have to travel all the way to the filament in order for electrons in the filament to start moving. Once the switch is turned on, the electric field makes its presence known to all of the electrons in the circuit essentially at the speed of light. It takes only a few nanoseconds for the electric field to affect the electrons in the filament after you turn on the switch.

Could anybody else please verify that the bit in bold is correct ?

 

[Tide]

Roger,

What, exactly, is your question about the statement? I would only qualify the word "immediately" as meaning longer than the time it takes light to travel, say, from one end to the other but didn't think it was necessary in the context of my note.

 

[Renge Ishyo]

My understanding roger is that the part you have bolded is correct. Can I verify it? Well, not really...

 

[roger]

I just wasn't sure whether or not Newtons law is valid for the electron.

 

[Tide]

Newton's laws of motion are valid as long as the speed of the electrons is much less than the speed of light which is certainly the case here - i.e. 100 V << 0.511 MeV.

 

[roger]

well, this is what I'm not sure about, which is why I would like someone else to support your statement.

 

[Tide]

Skepticism is a good thing!

While you're waiting for a reply I'll leave this thought with you: In a typcial electrical circuit such as one with a lightbulb the maximum potential difference is about 100 Volts so that no electrons can acquire energy greater than 100 Volts.

 

[Nam_Sapper]

I had an interesting discussion on the electric potential field with another EE recently.
He insisted (once he learned it) that the 'field' analogy was a far better explanation of what moves electrons in a wire than the 'water pressure' analogy, or the 'billiard ball' model, where the force from the electrical potential at one end of a resistor pushes the electrons along to the other end, bumping into each other and the odd nucleus along the way.

He almost hated the 'pressure' analogy for voltage. But this attitude is exaggerated. There are many situations where the 'EM' or "Electric Field' model of voltage and motivation for the electrons also fails utterly.

http://lentils.imagineis.com/rouge2/Plates-Voltage1.jpg

Here we can easily calculate the expected electric field caused by the voltage difference. But how is that supposed to motivate the electrons in a wire shaped as in the diagram below?

http://lentils.imagineis.com/rouge2/Plates-Voltage2.jpg

Here we have a field acting like a 'gravity' force, but unable to pull electrons through the wire. Just like a hanging hose full of water, the electrons are trapped. Whereas with the pressure-pipe analogy, the motion of electrons is easily explained by direct pressure and relative incompressibility of the electrons themselves. The repulsive field around the electrons is easily able to transfer the force of pressure from one end of the wire to the other.

 

[ZapperZ]

I'm starting to wonder at what point someone will point to:

(i) the semi-classical Drude model of charge transport;

(ii) the breakdown of such classical model in more exotic conditions and a full QM treatment has to be invoked;

(iii) the Boltzmann transport equation;

(iv) a solid-state physics text (such as Kittel or Ashcroft&Mermin) that covers Items (i), (ii), and (iii)?

I guess this point is here and now...

Zz.

 

[lightgrav]

It's not as fast as you think.
The E-field disturbance might propagate in a conductor at 1/2 c.
But that E-field is not disturbed by the closing of the switch -
it is caused by re-arrangement of charges in the conductor.
Unfortunately, that means current must begin near the switch,
which requires KE transport to occur (wait `till you see inductors).

 

[roger]

I'm starting to wonder at what point someone will point to:

(i) the semi-classical Drude model of charge transport;

(ii) the breakdown of such classical model in more exotic conditions and a full QM treatment has to be invoked;

(iii) the Boltzmann transport equation;

(iv) a solid-state physics text (such as Kittel or Ashcroft&Mermin) that covers Items (i), (ii), and (iii)?

I guess this point is here and now...

Zz.

But is Newtons law valid or not for the electron?

 

[lightgrav]

Classical electrons are subject to Newton's Laws of Motion (F=ma)
so long as you're carefuil to include ALL relevant Forces!
(yes, it's a tautology).

 

[arun_mid]

I'm starting to wonder at what point someone will point to:

(i) the semi-classical Drude model of charge transport;

(ii) the breakdown of such classical model in more exotic conditions and a full QM treatment has to be invoked;

(iii) the Boltzmann transport equation;

(iv) a solid-state physics text (such as Kittel or Ashcroft&Mermin) that covers Items (i), (ii), and (iii)?

I guess this point is here and now...

Zz.

well, after seeing the link you sent, I realized that asking for a rigorous mathematical description would be a little too deep for me...I'm not actually past classical theory yet...which was why I decided not to go further with the answers given, and to stick to analogy.

 

[Tide]

Zapper,

It's about context! Given the initial query and responses it's clear we're interested in the simplest explanation. Eschew obfuscation! ;)

 

[ZapperZ]

Zapper,

It's about context! Given the initial query and responses it's clear we're interested in the simplest explanation. Eschew obfuscation! ;)

But notice to the extent this is now being stretched. People are now asking whether "water pressure" or "billiard ball" model is valid, or if Newton's Laws are valid, etc. etc. I have given earlier a thread that essentially answered a question like this already. But it appears that it doesn't seem to satisfy a few people who seem to be looking for something "deeper"

That is why I decided that before they think a deeper description doesn't exist, I point out a very prominent source for such information that they can look up for themselves to their heart's content.

Zz.