Drude model with and without an electric field

In summary, the Drude model explains that without an electric field, no energy is transferred by electrons to ions. However, when an electric field is present, electrons gain energy and transfer it to ions. This is due to the assumption that the electrons immediately reach equilibrium after a collision, picking up just as much energy as they lose. The equation of motion for the electron includes a friction term and for DC, the relation to electric current is expressed as ##\sigma=\frac{e^2 n \tau}{m}##.
  • #1
aaronll
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Why in the Drude model without e-field no energy is transfer by electrons to ions, but when there is an e-field electrons transfer energy to ions ?
 
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  • #2
aaronll said:
Why in the Drude model without e-field no energy is transfer by electrons to ions
What, precisely, gives you that impression ?
One of the assumptions says
The electron is considered to be immediately at equilibrium with the local temperature after a collision.
i.e. the electrons pick up just as much energy as they lose.

##\ ##
 
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  • #3
BvU said:
What, precisely, gives you that impression ?
One of the assumptions says i.e. the electrons pick up just as much energy as they lose.

##\
that is clear, right, so with an electric field electron gain energy between collision and they transfer energy (kinetic energy) to lattice ion, and that energy is equal to the work done by the e-field on the electron?
So in "reality" electron gains velocity between collision but they lose that energy in collision and on average the velocity is the drift velocity?
 
  • #4
It's an effective description of an electron in the medium. The interaction with the medium is described by a linear friction term and thus the equation of motion for the electron reads
$$m \dot{\vec{v}}=-\frac{m}{\tau} \vec{v}-e \vec{E}.$$
If ##\tau## is small enough the velocity "relaxes" quickly to the equilibrium limit, where the force vanishes, i.e.,
$$\vec{v}=-\frac{e \tau}{m} \vec{E}.$$
Now for DC you assume the electrons within the conductor are all independent and then the relation to the elctric current is
$$\vec{j}=-e n \vec{v}=\frac{e^2 n \tau}{m} \vec{E} \; \Rightarrow \; \sigma=\frac{e^2 n \tau}{m}.$$
 
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FAQ: Drude model with and without an electric field

1. What is the Drude model?

The Drude model is a classical model used to describe the behavior of electrons in a metal. It assumes that the electrons behave like a gas of free particles and are subject to collisions with the metal ions.

2. How does the Drude model explain conductivity in metals?

The Drude model explains conductivity in metals by assuming that the electrons are constantly moving and colliding with the metal ions. These collisions cause resistance, but under the influence of an electric field, the electrons move in a directed manner, resulting in a net flow of charge and therefore, conductivity.

3. What is the difference between the Drude model with and without an electric field?

In the Drude model with an electric field, the electrons are subjected to an external force that causes them to move in a directed manner, resulting in a net flow of charge and conductivity. In the Drude model without an electric field, the electrons are still moving and colliding with the metal ions, but there is no net flow of charge and therefore, no conductivity.

4. How does the Drude model explain the temperature dependence of conductivity in metals?

The Drude model explains the temperature dependence of conductivity in metals by considering the effect of temperature on the average velocity of the electrons. As temperature increases, the average velocity of the electrons also increases, resulting in a higher conductivity due to more frequent collisions and a higher probability of electrons moving in a directed manner under an electric field.

5. What are the limitations of the Drude model?

The Drude model has several limitations, including: it does not take into account the quantum nature of electrons, it does not consider the effects of the crystal lattice on electron behavior, and it does not accurately predict the behavior of electrons at very low temperatures. It is also unable to explain the behavior of semiconductors and insulators.

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