Inhomogeneous Dielectric Question

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In summary, the problem involves finding an appropriate radial variation of the dielectric constant in order to make the E field independent of position between two coaxial conducting cylinders. The solution can be found by using Gauss's Law for dielectrics, where D=\epsilonE is substituted for the electric field. The approach involves choosing an arbitrary Gaussian surface inside the dielectric material and carrying out the integral to show that the E field is invariant. The solution can be easily obtained by finding the appropriate radial variation of the dielectric constant.
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Homework Statement



The space between two long coaxial conducting cylinders is filled with an inhomogeneous dielectric. Show that the E field can be made independent of position between the cylinders by an appropriate choice for the radial variation of the dielectric constant.

Homework Equations



I thought about starting with the "Gauss's Law" for dielectrics

where [tex]D=\epsilon E[/tex] is substituted for the electric field.

The Attempt at a Solution



My first approach was to try and calculate the electric field between the two cylinders by choosing an arbitrary Gaussian surface inside the dielectric material. But I'm not sure how to carry out that integral for this problem if I have to show the E field is invariant and I can't assume it.

Any tips or hints would be great, thanks!
 
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This was way easier than I made it out to be. I think I found the solution.
 

1. What is an inhomogeneous dielectric?

An inhomogeneous dielectric is a material that has varying dielectric properties, such as permittivity and conductivity, within its structure. This means that different parts of the material have different abilities to store and transmit electric charge.

2. What causes a dielectric material to become inhomogeneous?

There are several factors that can cause a dielectric material to become inhomogeneous, including structural variations, impurities, and external electric fields. These factors can lead to variations in the material's dielectric properties, resulting in an overall inhomogeneous structure.

3. How does an inhomogeneous dielectric affect electric fields?

When an electric field is applied to an inhomogeneous dielectric, the electric field lines will be distorted due to the varying dielectric properties of the material. This can result in non-uniform electric fields within the material, which can affect the overall behavior and performance of the material.

4. What are some applications of inhomogeneous dielectrics?

Inhomogeneous dielectrics have a wide range of applications in various fields, including electronics, telecommunications, and medical imaging. They are commonly used in devices such as capacitors, antennas, and MRI machines, where their ability to manipulate electric fields is crucial.

5. How do scientists study inhomogeneous dielectrics?

Scientists use a variety of techniques to study inhomogeneous dielectrics, including electrical measurements, microscopy, and computer simulations. These methods allow them to analyze the material's dielectric properties and better understand its behavior under different conditions.

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