Solving Linear Dielectric Eqns for E & P

In summary, for a linear dielectric with electric susceptibility χe and free charge density ρ, we can determine the resulting electric field by using the fact that ∫D\cdotda = Qfree-enclosed. This is possible because D = εE, where ε = ε0(1+χe). This allows us to account for the reduced electric field in a material with a different dielectric constant. However, it may seem magical that we are able to calculate the electric field or polarization with just this information.
  • #1
aaaa202
1,169
2
Say we have a linear dielectric with electric susceptibility χe a certain free charge density ρ. By using the fact that ∫D[itex]\cdot[/itex]da = Qfree-enclosed you can find the resulting electric field, because D = εE , where ε = ε0(1+χe).

The above is very weird for me. It seems to me that you are getting out too much information compared to how much you have at the start.

Let's look at it.

We know that the free charges will induce a certain polarization. These will in turn induce and electric field which induces a polarization and so on. This is not easy to break up to infinity but we find for linear dielectrics that the total electric field due to polarization such that:

E = ε0χeP

But how do we have any information that allows us to compute either the total field in the end or the total polarization? All we know is the field due to the free charges and the constant of proportionality between the total resulting field and P. It just seems magical to me that you are actually able to calculate E or P with just this information.
 
Physics news on Phys.org
  • #2
[itex]\vec{P}=\epsilon_{0}\chi_{e}\vec{E}[/itex]
[itex]\vec{D}=\epsilon_{0}\vec{E}+\vec{P}=\epsilon_{0} \chi_{e}\vec{E}+\epsilon_{0} \vec{E}=\epsilon \vec{E}=\epsilon_{r} \epsilon_{0}\vec{E}[/itex]

Basically, this is simply a way to account for the apparent reduced E field in a material of different dielectric constant. At least that's how I think of it.
 
Last edited:

1. What are linear dielectric equations?

Linear dielectric equations are mathematical equations that describe the behavior of electric fields and polarization in a material. They are used to understand and predict the response of a material to an external electric field.

2. How do you solve linear dielectric equations?

To solve linear dielectric equations, you need to first determine the electric field and polarization in the material. This can be done by using boundary conditions and known properties of the material, such as its dielectric constant. Then, you can use mathematical methods such as Gaussian elimination or matrix inversion to solve for the unknown variables.

3. What is the significance of solving linear dielectric equations?

Solving linear dielectric equations allows us to understand the behavior of electric fields and polarization in different materials. This knowledge is essential in many applications, such as designing electronic devices and understanding the properties of materials used in technology.

4. What are some common applications of solving linear dielectric equations?

Some common applications of solving linear dielectric equations include designing capacitors, calculating the dielectric constant of materials, and predicting the behavior of dielectric materials in electric fields. They are also used in the study of electromagnetism and electronic circuits.

5. Are there any limitations to using linear dielectric equations?

Linear dielectric equations are only applicable to materials that exhibit a linear relationship between the electric field and polarization. This means that they may not accurately describe the behavior of materials under very high electric fields or in non-linear materials. Additionally, they do not take into account factors such as temperature and frequency, which can also affect the behavior of materials.

Similar threads

Replies
5
Views
825
  • Electromagnetism
Replies
6
Views
767
Replies
3
Views
652
  • Electromagnetism
Replies
1
Views
811
Replies
5
Views
1K
Replies
16
Views
1K
Replies
3
Views
637
  • Electromagnetism
Replies
1
Views
2K
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
14
Views
499
Back
Top