Electrochemical potential and negative Hall resistance

[barefeet]

Homework Statement

In the case of the b trajectories, I want to understand why the electrochemical potential at voltage contact 3 must be the same as the current contact 4. And can you say anything about the electrochemical potential inside the sample itself?

Homework Equations

- I know that a voltage contact adjusts its electrochemical potential to the value needed to create a net current of 0.

- I know that electrons move from a high electrochemical potential to a low electrochemical potential.

The Attempt at a Solution

I could say that the net current between 4 and 3 is 0, so the potentials must be the same. But there is also no net current between 4 and 1, so why can't you say the same about the potentials of 4 and 1. And also between 2 and 3. And what is the potential inside the sample itself

 

[mark726]

?

I can provide some insights into the electrochemical potential at voltage contact 3 and current contact 4. First, it is important to understand that electrochemical potential is a measure of the energy required to move a unit of charge from one point to another. In the case of a battery, the electrochemical potential is a measure of the energy difference between the anode and cathode.

In this scenario, the voltage contact 3 is connected to the anode, while the current contact 4 is connected to the cathode. Since there is a flow of electrons from the anode to the cathode, it can be assumed that the electrochemical potential at the anode is higher than that at the cathode. This difference in potential creates an electric field, which drives the flow of electrons and creates a current.

Now, why must the electrochemical potential at voltage contact 3 be the same as current contact 4? This is because both contacts are connected to the same battery, which means they are at the same potential. In other words, the battery maintains a constant potential difference between the anode and cathode, and any point connected to these two points will have the same potential.

As for the electrochemical potential inside the sample itself, it will depend on the composition and structure of the sample. If the sample is a conductor, the electrochemical potential will be constant throughout the sample. However, if the sample is a semiconductor or insulator, there may be variations in the electrochemical potential due to differences in the material's band structure.

In conclusion, the electrochemical potential at voltage contact 3 must be the same as current contact 4 because they are connected to the same battery. The potential inside the sample will depend on the material's properties and can vary throughout the sample.