What is the electric displacement field for one electron?

In summary, the electric displacement field is a vector field that describes the amount of electric flux per unit area passing through a given point in space. It is related to the electric field by the equation D = ε0E + P, and is significant in understanding the behavior of electric charges. The electric displacement field for one electron can be calculated using the equation D = Q/4πε0r^2, and has many real-world applications such as in electronic devices and the study of electromagnetic waves.
  • #1
Damned charming :)
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I am teaching myself Maxwells equations for fun and this question may be gibberish but I would like to know know the explicit formula for D for a single elecron so I can practice my use of the divergence theorem and check the divergence is the charge density.
 
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  • #2
The Electric Displacement vector, D, will depend on the surrounding material. The formula for D is just the permittivity of the surrounding material multiplied by E (in S.I. units).

Claude.
 
  • #3


The electric displacement field, also known as D-field, is a concept in electromagnetism that describes the electric flux density per unit area. It is defined as the electric field plus the polarization density, which is the electric dipole moment per unit volume of a material.

For a single electron, the electric displacement field can be expressed as D = ε0E + P, where E is the electric field and ε0 is the permittivity of free space. Since a single electron has a charge of -e, the divergence of the electric displacement field can be calculated as:

∇ · D = ∇ · (ε0E + P) = ∇ · ε0E + ∇ · P = ρ/ε0 + ρp

where ρ is the charge density and ρp is the polarization charge density.

In the case of a single electron, there is no polarization charge density because there is no dipole moment. Therefore, the divergence of the electric displacement field reduces to:

∇ · D = ρ/ε0

This shows that the divergence of the electric displacement field for a single electron is equal to the charge density divided by the permittivity of free space.

In terms of the explicit formula for D, it can be written as D = ε0E - eδ(r), where δ(r) is the Dirac delta function representing the point charge of the electron. This formula takes into account the contribution of the electron's charge to the electric displacement field.

In summary, the electric displacement field for a single electron is given by D = ε0E - eδ(r), and its divergence is equal to the charge density divided by the permittivity of free space.
 

1. What is the electric displacement field?

The electric displacement field is a vector field that describes the amount of electric flux per unit area passing through a given point in space. It is represented by the symbol D and is measured in units of coulombs per square meter (C/m^2).

2. How is the electric displacement field related to the electric field?

The electric displacement field is related to the electric field by the equation D = ε0E + P, where ε0 is the permittivity of free space and P is the polarization vector. This equation takes into account the effects of both free and bound charges on the electric displacement field.

3. What is the significance of the electric displacement field for one electron?

The electric displacement field for one electron represents the electric flux per unit area due to the presence of a single electron in space. This field is important in understanding the behavior of electric charges and their interactions with each other and their surroundings.

4. How is the electric displacement field for one electron calculated?

The electric displacement field for one electron can be calculated using the equation D = Q/4πε0r^2, where Q is the charge of the electron, ε0 is the permittivity of free space, and r is the distance from the electron to the point where the field is being measured.

5. What are some real-world applications of the electric displacement field?

The electric displacement field has many real-world applications, including in the design and analysis of electronic devices, the understanding of the behavior of materials under electric fields, and the study of electromagnetic waves and their propagation. It is also used in the development of technologies such as capacitors, dielectric materials, and optical fibers.

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