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

In summary, the conversation discusses the derivation of a formula from Newton's 2nd law and the Drude assumption. It is mentioned that the Drude formula contains an error, which has been known for many years.
  • #1
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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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  • #2

1. What is Newton's 2nd Law and how does it relate to conductivity?

Newton's 2nd Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In terms of conductivity, this means that the current (which is a measure of acceleration of charge) is directly proportional to the applied electric field (net force) and inversely proportional to the material's resistance (mass).

2. What is the Drude assumption and why is it important for understanding conductivity?

The Drude assumption is a simplifying assumption made in the classical model of electrical conductivity. It states that the electrons in a material behave like a gas, moving randomly and colliding with other particles. This assumption is important because it allows us to use classical mechanics to understand the behavior of electrons in a material, making calculations and predictions easier.

3. How does the Drude assumption explain the difference in conductivity between metals and insulators?

The Drude assumption explains the difference in conductivity between metals and insulators by considering the behavior of electrons. In metals, the electrons are free to move around and are not bound to specific atoms, allowing for easy flow of charge. In insulators, the electrons are tightly bound to their atoms and are not free to move, resulting in low conductivity.

4. Can Newton's 2nd Law and the Drude assumption be applied to all materials?

No, Newton's 2nd Law and the Drude assumption are only applicable to materials that follow classical mechanics. They do not apply to materials at the quantum level, such as semiconductors, which require a different set of equations and assumptions to understand their conductivity.

5. How does temperature affect the conductivity of a material?

Temperature affects the conductivity of a material in two ways. First, as temperature increases, the atoms in a material vibrate more, making it harder for electrons to move through the material, resulting in decreased conductivity. Second, at higher temperatures, some materials can undergo changes in their crystal structure, altering the arrangement of atoms and changing their conductivity properties.

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