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I have a doubt about the understanding of drift velocities in a current. My problem is that the textbook speaks very loosely about this. It's like: "well, if we apply a field $E$ then the charges will experience a force due to this field, aquire acceleration, colide between then and because of that there will be a small resultant velocity for each particle called drift velocity".

But wait a moment, how can we be so sure of all of that? For me it's a little counterintuitive, and even if it was intuitive, how can we show that this really occurs? In other words, I feel that the first step to understand the meaning of drift velocity is to be really sure that this velocity will exist.

And once we've shown it exists, what's is this velocity anyway? Is the velocity of the particle in the direction of the current?

Thanks a lot in advance for your help!

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I think your questions concerns somehow another question: what is the relation between the macroscopic observables (like electrical current, temperature) of system consisting of many particles and parameters of single particles forming this system. The answer on this question is given by statistical physics. First, it will be useful to think about an electron gas in a metal wire without any current. There is no current, but I dare you all particles are moving if the temperature is not equal zero. The electrical current results from averaging of velocities of all charge carriers and, therefore, equals zero. If we apply voltage all electrons gain an additional component to their chaotic velocities in the direction of the electric field. We have got electron drift, however it is not equal to microscopic current of each electron.

Is the velocity of the particle in the direction of the current?

It depends on the charge sign of charge carriers. If we have got electrons then their averaged speed is opposite to the direction of the electrical current.

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I understood what you said, but then why due to the field there is no net acceleration of the electron gas in the direction of the field, but there is only a constant velocity? –  Satwik Pasani Jun 22 '13 at 15:27
    
Interesting question! Does electron flow in wire with finite resistance represent ergodic system? –  freude Jun 23 '13 at 13:23
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