Does the Drude Model Account for J Cross B Force in Hall Conductivity?

In summary, the conversation discusses the concept of hall conductivity and the generation of a hall current due to the presence of a magnetic field and an electric field perpendicular to it. It is noted that this current can result in negative conductivity if the effect is strong enough and if electrons have sufficient thermal energy in a plasma. However, the Drude model equation does not give negative conductivity, leading to a discussion about whether the model does not consider the J cross B force. It is also mentioned that the MHD analysis should be used for a plasma instead of the Drude model. The conversation ends with a remark about the challenges of selecting and utilizing hot electrons with a wider Gaussian velocity distribution.
  • #1
chandrahas
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I was thinking about hall conductivity, when this question popped up. If there is a magnetic field and an electric field perpendicular to it, then a hall current is generated since the ions have larger gyro radii compared to electrons. Now this current would produce a J cross B force in the direction of Electric field. this means that if electrons have sufficient thermal energy in a plasma, they can create a current that pushes them in the direction of the electric field. This would result in negative conductivity if it is strong enough right?

But solving the drude model equation doesn't give us and negative conductivity anywhere.

So, I was wondering if the effect is not strong enough to result in negative conductivity or whether the drude model does not consider the J cross B force. I always thought the momentum- magnetic field cross product term was the J cross B force.

Thanks
 
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  • #2
chandrahas said:
Now this current would produce a J cross B force in the direction of Electric field. this means that if electrons have sufficient thermal energy in a plasma, they can create a current that pushes them in the direction of the electric field. This would result in negative conductivity if it is strong enough right?
The Drude model assumes a solid state. I would not apply the Drude model to a plasma. In a plasma you must use MHD analysis.
Hot electrons have a wider Gaussian velocity distribution. Only a few will be going against the flow, an equal number will be going faster by a similar amount.
 
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  • #3
Baluncore said:
an equal number will be going faster by a similar amount.
Oh, if only we could select those and use them.
 

FAQ: Does the Drude Model Account for J Cross B Force in Hall Conductivity?

1. What is the Drude model?

The Drude model is a classical model used to describe the behavior of electrons in a metal. It was developed by physicist Paul Drude in the late 19th century and is based on the assumptions that electrons are free to move and collide with each other and the metal ions.

2. How does the Drude model explain electrical conductivity?

The Drude model explains electrical conductivity by considering the movement of free electrons in a metal. When an electric field is applied, the electrons accelerate and collide with other electrons and the metal ions, transferring energy and momentum. This flow of electrons results in the flow of electric current.

3. What are the limitations of the Drude model?

The Drude model is a simplified model and does not take into account the quantum nature of electrons. It also does not consider the effects of electron-electron interactions and the crystal lattice structure of the metal. These limitations make it less accurate for describing the behavior of electrons in metals at very low temperatures or in highly conductive materials.

4. How does the Drude model explain the thermal conductivity of metals?

The Drude model explains thermal conductivity by considering the movement of electrons in response to a temperature gradient. As the temperature increases, the electrons gain kinetic energy and collide more frequently with other particles, transferring energy and increasing the thermal conductivity of the metal.

5. Can the Drude model be applied to non-metals?

The Drude model is primarily used for metals, as it is based on the assumption of free electrons. However, it can also be applied to some non-metallic materials such as semiconductors and insulators, as long as they have a sufficient number of free charge carriers. In these cases, the Drude model may need to be modified to account for additional factors such as band structure and electron-electron interactions.

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