Understanding Newton's 2nd Law & Drude Assumption for Conductivity

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SUMMARY

This discussion centers on the derivation of the Drude model for electrical conductivity using Newton's 2nd Law. The equation m dv/dt = -eE is established, leading to the average velocity of an electron = -meEτ/2, where τ represents the average time between scattering events. The participant identifies a discrepancy in the Drude formula, noting that the conductivity should not include the factor of ½. This error is acknowledged as a common point of confusion within the physics community.

PREREQUISITES
  • Understanding of Newton's 2nd Law of Motion
  • Familiarity with the Drude model for electrical conductivity
  • Knowledge of electron dynamics in electric fields
  • Basic concepts of average velocity and scattering time (τ)
NEXT STEPS
  • Study the derivation of the Drude model for conductivity in detail
  • Explore the implications of scattering time (τ) on electron mobility
  • Investigate common misconceptions in the Drude model and their resolutions
  • Review experimental validations of the Drude model against modern theories
USEFUL FOR

Physics students, electrical engineers, and researchers interested in solid-state physics and the behavior of electrons in conductive materials.

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I can't derive it properly even though it should be easy:
From Newtons 2nd law:

m dv/dt = -eE

=>

v(t) = -meEt + v(0) (the latter will average out when taking average)

Now the Drude assumption: An electron will on average travel a time τ before being scattered and starting its motion in the direction of E all over.

Thus this means, I think, that on average an electron will travel with a velocity equal to
<v> = -meEτ/2

And one can then multiply by electron density to get the Drude formula. Problem is the conductivity should not have the factor ½. Am I not right in thinking that the electron on average will travel at the velocit given above.
 
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