Why Does Potential Drop Occur Outside Metal in Electric Fields?

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I have read this paragraph:
[...]
"When an electrical field is applied to a metal, a potential drop associated with that field must take place outside the metal, usually at the metal contacts: any change in potential inside the metal is prevented by the mobility and number density of the carriers. This can be understood from Poisson equation"
(Hamnett and Christensen)

I have some question which need your help:
1. Why potential drop must "take place outside" the metal ?
2. Why "mobility and density of carriers" prevent such thing to happen?
3. Poisson equation is the second derivative of the potential in the x direction = -p (epsilon*const) where p = density of charge carrier and epsilon = dielectric function of the semiconductor. What are the relation between this equation the above paragraph?

Thank you very much!

 

[Valerie Park]

1. Potential drops take place outside the metal because of the presence of the electrical field, which causes a charge to be transferred from one point in the metal to another. This transfers energy from one point to another, and this energy is then dissipated as heat or light when the charge reaches the metal contacts. 2. The mobility and number density of carriers prevent a change in potential inside the metal because the charge carriers are able to move freely through the metal, and the number of charge carriers is relatively constant. Thus, any excess charge that is transferred from one point to another is quickly balanced out by the movement of the charge carriers. 3. Poisson equation describes how the electrical potential varies with position in a given region. It can be used to determine the potential drop associated with an applied electrical field, since it takes into account the density of charge carriers and the dielectric function of the semiconductor. Thus, it can be used to explain why potential drops take place outside the metal, as well as why changes in potential inside the metal are prevented by the mobility and number density of the carriers.

 

[sir-pinski]

1. The potential drop must take place outside the metal because metals have a high density of free electrons that are able to move easily in response to an electric field. This means that any potential changes within the metal would be quickly neutralized by the movement of these electrons. Therefore, the potential drop occurs outside the metal where there are less free electrons and the electric field is able to have a larger effect.

2. The mobility and density of carriers in a metal are very high, meaning that the electrons are able to move easily and there are a large number of them. This makes it difficult for a potential drop to occur within the metal because the electrons are able to quickly compensate for any changes. It is similar to trying to change the water level in a large pool - even if you add or remove a small amount of water, it will quickly spread out and return to its original level.

3. The relation between the Poisson equation and the above paragraph is that the Poisson equation helps to explain the behavior of the potential within a material. In this case, it is used to show how the potential changes within a metal when an electric field is applied. The equation takes into account the density of charge carriers and the dielectric function of the material, both of which are mentioned in the paragraph.