Electric field distribution in a conductor with moving charges

In summary, understanding the concepts of electric fields in conductors and dielectrics requires considering the permittivity of materials and the distribution of potential in different media. It may seem counterintuitive that electric fields can exist in conductors, but the key is understanding the role of charge carriers and their potential.
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I'm trying to reconcile some concepts in electrostatics and dynamics to do with electric fields in conductors.

The relative permittivity (constant) of a material seems to be determined by it's ability to be polarized and subsequently induce an electric field within a conductor or dielectric. The permittivity (constant) of a vacuum seems to merely facilitate the calculation of the electric field (voltage) at some distance from a charge or group of charges.

When looking at the electric field in a vacuum some distance from point charge/s, there doesn't seem to be any sort of attenuative effect other than the electric field strength diminshing due to the distance from the point charge (characterised by a the ubiquitous steradian 1/(4[tex]\pi[/tex]r2) function).

I guess the implication here is that lower permittivity constants in dielectrics and insulators result in the speed of electromagnetic wave propagation through these media being lower than the speed of light.

The implication here is that the electric field can propagate through any medium in the absence of motion of charge carriers. This seems counterintuitive though.

Imagine for instance a voltage source (say a bunch of static charges) connected to a strong dielectric (so that the charge cannot spread along the wire) and a long wire. Can you measure the voltage at the end of this wire using a device with an infinite input impedance? I would have thought that you need a small amount of charge to flow into the measuring device to be able to ascertain the electric field at the end of the wire.

Conventional circuit theory would tell you that the voltage at the end of the wire is the same as the voltage at the start of the wire in the absence of moving charges. However, if you consider the attenuation of the electic field due to permittivity considerations, one would expect the voltage at the end of the wire to be lower as the electric field is attenuated by the conductor.

I'm struggling to find an intuitive explantion of how potential distributes itself in media other than a vacuum. What does it mean to say that the potential drops across a circuit loop proportionally based on the current flowing and resistance of the loop?

How are charge carriers imbued with potential that they can shed through collisional processes whilst drifting through a conductor? Assuming that the charge carriers themselves have potential that can be lost seems incongruent with the conductor having an electric field distribution through it based on it's permittivity.
 
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  • #2
The basic concepts of electrostatics and dynamics are quite simple and intuitive, but when you start to consider media, permittivity, and other factors, it can become quite daunting. The key to understanding this is to remember that electric fields are present in all materials, even in conductors (though they are attenuated). Charge carriers in a conductor are imbued with potential which they can shed through collisions with other particles. This potential is then distributed throughout the conductor based on the permittivity of the material. Finally, conventional circuit theory tells us that the voltage across a circuit loop is proportional to the current flowing and resistance of the loop.
 
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I can provide some insights on the concepts you are trying to reconcile. First of all, it is important to understand that the electric field is a fundamental property of space and is not dependent on the presence of charges. It exists even in a vacuum and is responsible for the interactions between charges.

In a conductor, the presence of moving charges (electrons) creates an electric field that is in equilibrium with the external electric field. This is known as the "skin effect" and it results in the charges being distributed on the surface of the conductor. The permittivity of the material plays a role in this process by determining how easily the charges can move and redistribute themselves.

The concept of relative permittivity or dielectric constant is important when considering the propagation of electromagnetic waves through a medium. This is because the electric field in a medium is affected by the presence of charges and their ability to respond to the external electric field. This results in a decrease in the speed of propagation compared to the speed of light in a vacuum.

In your example of a voltage source connected to a strong dielectric and a long wire, the voltage at the end of the wire would indeed be the same as the voltage at the start of the wire. This is because the charges in the wire are in equilibrium and there is no net flow of charge. The electric field inside the wire is also constant, as long as the wire is of uniform cross-section and material.

Regarding the potential distribution in media other than a vacuum, it is important to understand that potential is a measure of the work done in moving a unit charge from one point to another. In a conductor, the potential is constant throughout as there is no net flow of charge. In a circuit with resistors, the potential drops occur due to the work done in overcoming the resistance of the material. This is what is meant by the potential dropping proportionally based on the current flowing and resistance of the loop.

Lastly, the concept of charge carriers shedding potential through collisional processes is related to the movement of electrons in a conductor. As electrons move, they collide with the atoms of the material, losing some of their energy and contributing to the overall resistance of the material. This does not contradict the fact that the conductor has an electric field distribution based on its permittivity. The two concepts are interconnected and work together to maintain the equilibrium of charges in the conductor.

In conclusion, the concepts of electric field, permittivity, and potential
 

1. What is an electric field distribution in a conductor with moving charges?

The electric field distribution in a conductor with moving charges refers to the pattern of electric fields that is created within a conductor when there are charges moving through it. This distribution is affected by the movement of charges and the properties of the conductor, and is important in understanding the behavior of electric currents.

2. How does the electric field distribution change in a conductor with moving charges?

The electric field distribution in a conductor with moving charges will change depending on the velocity and direction of the moving charges, as well as the material and geometry of the conductor. It can also be affected by external electric fields.

3. What is the significance of the electric field distribution in a conductor with moving charges?

The electric field distribution in a conductor with moving charges is important because it determines the flow of electric currents within the conductor. It also affects the amount of resistance and heat generated in the conductor, which can impact the efficiency and safety of electrical systems.

4. How is the electric field distribution measured in a conductor with moving charges?

The electric field distribution in a conductor with moving charges can be measured using devices such as voltmeters or ammeters, which can detect changes in electric potential or current. It can also be calculated using mathematical equations and modeling techniques.

5. What factors affect the electric field distribution in a conductor with moving charges?

The electric field distribution in a conductor with moving charges is affected by a variety of factors, including the velocity and direction of the moving charges, the material and geometry of the conductor, the presence of external electric fields, and the properties of the surrounding environment. It can also be influenced by temperature, humidity, and other external factors.

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