Revered Members,
The drift velocity is of the order 0.1 cm/s. If the drift velocity is of such small magnitude, how conductors maintain a continuous flow of electrons?

 

An amp is 6.241 × 10E18 electrons passing a set point per second. This is a very large number of electrons, they do not have to go fast.

http://en.wikipedia.org/wiki/Ampere

 

Because the electrons are just charge carriers (for the real/virtual photon electromagnetic force) they don't have to really move (from one end of the wire to the other) at all to carry current. The electron drift velocity in a AC circuit is zero as the free electron gas from the metal ions just vibrates back and forth.

http://en.wikipedia.org/wiki/Speed_of_electricity

Photons always travel at the the speed of light. In a medium like a wire the propagation speed is less as there is a delay as the photons are absorbed and reemitted by matter.

 

Revered Members,
The drift velocity is of the order 0.1 cm/s. If the drift velocity is of such small magnitude, how conductors maintain a continuous flow of electrons?

This is a "loaded" question. (http://en.wikipedia.org/wiki/Loaded_question)

The value of the drift velocity is independent of the explanation of why a conductor can maintain a continuous flow of electrons.

Conductors maintain a continuous flow of electrons because the electrons are free to move, there are many of them and because they flow in a circuit. You can't run out of electrons if they loop around in a circuit. The number of charges and the speed of the charges determine the value of current, not whether they flow continuously.

Also, at a fundamental level, they flow discretely, but are only approximated as continuous flow.

 

And let's not forget that the energy flow comes because each electron that moves pushes the electric field with propagation speed of the speed of light (in the medium, coax, PCB etc.) so the energy mostly goes because of electric field. The energy coming out the goesoutof end is because all those electrons did the wave and pushed neighbors starting at the goesinto end.

 

I've always found the marbles-in-a-tube analogy to be misleading. Think about it: the metal in wire is neutrally charged. For every electron pushing you from behind there's a proton nearby pulling you back just as hard.

Reality is more complicated, but it's not that bad and I don't see why most introductory texts leave this out. My understanding of what's really going on is this (sources at the end):

1) A voltage source adds electrons at one place and removes electrons at another place in the circuit (such as at the battery terminals).

2) This redistribution of charge affects the electric field through the region at the speed of light.

3) This electric field causes the mobile electrons in the conductor to drift. They rearrange themselves in such a way that all charge excess or charge deficiency ends up at the surfaces of the conductors. The interior regains its neutrality in the steady-state case.

4) This forms a surface charge gradient along the length of the conductor, which sets up an electric field inside the conductor that is everywhere parallel to the conductor, even as it bends and turns.

5) This resulting electric field is what drives the conducting electrons to drift together as current.

6) Energy flux is zero inside the conductor (metal conducts current but not energy). Energy is "actually" transported in the EM field outside the conductors.

Sources:

Chabay and Sherwood, Matter and Interactions Volume 2

J.H. Poynting (1883), On the Transfer of Energy in the Electromagnetic Field

 

I've always found the marbles-in-a-tube analogy to be misleading. Think about it: the metal in wire is neutrally charged. For every electron pushing you from behind there's a proton nearby pulling you back just as hard.

This is actually incorrect. If the electrons are locked down the material / element is an insulator, but with metals the outer electrons float, they move where they wish easily, usually in a random fashion. This is what makes them a conductor, the presence of an electric field make them drift in a specific direction. If you start talking about individual atoms it becomes more true, but metals usually have a structure, be it crystal or other. Ever look at metals under high power they are granular.

 

But for a given small volume of conductor the number of electrons (mobile or not) is equal to the number protons, on average. Beyond a distance of a few atoms, the mobile electron charges are well-screened. Steady-state current is maintained by surface charge gradients, not electrons pushing from behind in the interior of a conductor.

 

Again, slightly off. With a conductor a charge (excess electrons or minimum electrons) still distribute themselves evenly through out the material because of the electron mobility. With an insulator the electrons can not redistribute themselves, and this is a static (as in static electricity) charge on the surface of the material.

Since the imbalance is distributed evenly across the surface it is much more likely to be equalized. As in a vacuum tube an electron can go ballistic, or in a conductive atmosphere an electron can leave the material.

 

With a conductor a charge (excess electrons or minimum electrons) still distribute themselves evenly through out the material because of the electron mobility.

Maybe I'm mis-reading this, but this is backwards. Excess charge in a conductor will apply a coulomb force (unscreened because the charges aren't balanced) which will cause the mobile charges to redistribute in such a way that the excess immediately migrates to the surface.

Quote from the Chabay and Sherwood textbook I referenced: "...any excess charge on a piece of metal, or any conductor, are always found on an outer or inner surface."

If I've been taught by crappy sources, please let me know ASAP.

 

Maybe I'm mis-reading this, but this is backwards. Excess charge in a conductor will apply a coulomb force (unscreened because the charges aren't balanced) which will cause the mobile charges to redistribute in such a way that the excess immediately migrates to the surface.

Quote from the Chabay and Sherwood textbook I referenced: "...any excess charge on a piece of metal, or any conductor, are always found on an outer or inner surface."

If I've been taught by crappy sources, please let me know ASAP.

You are correct.

http://www.astrophysik.uni-kiel.de/~hhaertel/PUB/voltage_IRL.pdf

 

That's a cool document. It does illustrate, however, that conductors can contain interior excess charge in regions where bulk resistivity is changing (such as at the ends of a resistor) in the non-equilibrium case of flowing charge.

Bottom line, for the OP's question: the surface charge distribution reacts at the speed of light, but the interior charges representing current only move at drift velocity. The surface charge distribution maintains the steady flow of charges.

 

That's a cool document. It does illustrate, however, that conductors can contain interior excess charge in regions where bulk resistivity is changing (such as at the ends of a resistor) in the non-equilibrium case of flowing charge.

Sure, those internal charge regions show the flow of energy (seen as heat in a resistor) into the material instead of space at those points. It also shows that energy/charge moves (like a lightwave) from both ends of the battery into the load while the charge carriers (slowly) circulate round.

 

I'm not sure whether this warrants a new thread but is closely related to the topic under discussion.
As we all know resistivity & hence resistance, in metals GENERALLY increases with temperature (and superconductivity happens as we approach 0 Deg. K ) This has always seemed odd to me considering that the electrons in the outer orbits are in a more excited state and should be more mobile with increasing temperature.
Any ideas anyone?

 

It's mainly caused (in Semiconductors) by mechanical wave effects changing electron mobility.

Lattice (phonon) scattering
At any temperature above absolute zero, the vibrating atoms create pressure (acoustic) waves in the crystal, which are termed phonons. Like electrons, phonons can be considered to be particles. A phonon can interact (collide) with an electron (or hole) and scatter it. At higher temperature, there are more phonons, therefore increased phonon scattering which tends to reduce mobility.

http://en.wikipedia.org/wiki/Electron_mobility#Temperature_dependence_of_mobility

 

As we all know resistivity & hence resistance, in metals GENERALLY increases with temperature. This has always seemed odd to me considering that the electrons in the outer orbits are in a more excited state and should be more mobile with increasing temperature.
Any ideas anyone?

Professor Lewin's lecture on Ohms law helps give you an idea about this. In a nutshell, a simple classical model shows conductivity is proportial to the time between collisions. High temperature implies shorter time between collisions and lower conductivity.

As the Professor points out, you really need quantum mechanics to derive this more rigorously. But this classical description is good for getting an intuitive feel, which seems to be what you are asking for.

http://ocw.mit.edu/courses/physics/.../lecture-9-currents-resistivity-and-ohms-law/


Keep in mind that in semiconductors (at least intrinsic ones), the effect is opposite. Higher temperature causes a higher rate of excitation of the electrons into the conduction band (leaving a hole in the valence band) and results in lower resistance since the hole and the electron are now free charges contributing to conduction.