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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.
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.