Dielectric Sphere with Free Volume Charge

In summary, a dielectric sphere with free volume charge is a spherical object made of a material that is a good insulator and contains free charges within its volume. When placed in an external electric field, it will polarize and create an induced electric field inside the sphere that opposes the external field. The polarization is directly proportional to the electric field strength inside the sphere. This type of sphere can store electric energy by creating an energy barrier when placed in an external field, and its ability to store energy is related to its high permittivity.
  • #1
jegues
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Homework Statement



See figure attached.

Homework Equations





The Attempt at a Solution



I'm confused as to how they got their D(r)

Using Gauss' Law,

For r < or = a

[tex]\oint_{S} \vec{D} \cdot \hat{n} dS = \int_{v} \rho dv [/tex]

[tex]D(4 \pi r^{2}) = \frac{\rho 4 \pi r^{3}}{3}[/tex]

[tex]\Rightarrow D = \frac{P_{0}r^{2}}{3a}[/tex]

What am I doing wrong?
 

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  • #2
You have ρ = constant. It's not.
 

Related to Dielectric Sphere with Free Volume Charge

1. What is a dielectric sphere with free volume charge?

A dielectric sphere with free volume charge refers to a spherical object made of a material that is a good insulator, also known as a dielectric. It contains free charges within its volume, which can move and create an electric field inside the sphere.

2. How does a dielectric sphere with free volume charge behave in an electric field?

When placed in an external electric field, a dielectric sphere with free volume charge will polarize, meaning the free charges within the sphere will orient themselves in response to the field. This results in an induced electric field inside the sphere that opposes the external field, making the sphere less affected by it.

3. What is the relationship between the polarization and electric field inside a dielectric sphere with free volume charge?

The polarization of a dielectric sphere with free volume charge is directly proportional to the electric field strength inside the sphere. This means that as the external electric field increases, so does the induced electric field within the sphere.

4. Can a dielectric sphere with free volume charge store electric energy?

Yes, a dielectric sphere with free volume charge can store electric energy. When placed in an external electric field, the induced electric field inside the sphere creates an energy barrier, allowing the sphere to store energy. This stored energy can be released when the external field is removed.

5. How is the permittivity of a dielectric sphere with free volume charge related to its ability to store electric energy?

The permittivity of a material measures its ability to store electric energy. A higher permittivity means a material can store more energy. As a dielectric sphere with free volume charge is made of a material with high permittivity, it has a high capacity to store electric energy.

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