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Drift velocity is defined as :

$$V_{dx}=\frac{e \tau}{m_e} E_x$$

Therefore, mean time between collisions is τ= $\frac{m*v(drift)}{eE} $ however, τ is also τ=$\frac{\Lambda}{<v>} $ in which $<v>$ is average speed of electrons and $\lambda$ is mean free path. average speed is larger and has an inverse relationship with τ.I guess because it is thermal average energy? drift velocity on the other hand has a direct relationship and is smaller.

my question is: how is drift velocity related to average speed? and also what is the difference between the τ in the two formulas? can I use the drift velocity to get τ?
is τ=$\frac{\Lambda}{<v>} $ related to a single collision rather than many collisions over time?

Qmechanic
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olly
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1 Answers1

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The thermal (random) speed of free electrons in copper at room temperature is of the order $10^5$ m/s. The electrons collide with themselves and with the lattice made up of copper ions and are in thermal equilibrium with no net transfer of kinetic energy between them.
When an electric field is applied which causes an electric current to flow there is a drift velocity imposed on the random motion of the electrons which is very much less ($\approx 10^{-5}$ m/s) than the thermal speed - demonstrated here and here is an animation to illustrate the effect of an electric field on the free electrons with the thermal speeds being comparable with the drift speeds! If the speed scaling was correct (order of magnitude difference $10^{10}$) you would not see any difference between there being no electric field applied and an electric field being applied.

In the Drude model the assumption is made that after collision with the lattice an electron which had gained some extra energy from the electric field between collisions loses all of the extra energy to the lattice ions and there is some average time between collisions.

If the thermal speeds increase due to an increase in temperature, the metal ions in the lattice vibrate more and impede the drift of the free electrons under the influence of an electric field more with the result that the drift speed (current) is decreased. The resistance of the metal has increased.

Farcher
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