Electric field in a dielectric material

In summary, the problem involves finding the electric field within a long cylinder of linear dielectric material in a uniform electric field. The general solution of Laplace's equation in cylindrical coordinates with azimuthal symmetry should be used, and the length of the cylinder should not be assumed to be approaching infinity. The electric field can be found by using the general solution and taking the derivative of the potential with respect to r.
  • #1
noblegas
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0

Homework Statement



A very long cylinder of liner dielectric materil is placed in an otherwise uniform electric field [tex]E_0[/tex] . Find the resulting field within the cylinder. (the radius is a , the susceptibililty [tex]\chi_e[/tex] and the axis is perpendicular to [tex]E_0[/tex])

Homework Equations


The Attempt at a Solution



[tex]V_in(r,\theta)= \sigma(l=0..infinity)A_l*r^l*P_l(cos(\theta)[/tex]

should I take the derivative of [tex]V_in[/tex] with respect to r to obtain the field? Not sure why latex isn't display infiinity but l is supposed to range from zero to infinity

I also know that [tex]E_0[/tex] = [tex]\lambda/(2*\pi*\epsilon_0*a)[/tex]

[tex]P_0=\epsilon_0*\chi_e*E_0[/tex] [tex]P=\epsilon*\chi_e*E[/tex] ; should I plugged [tex]\chi_e=P/(E_0*\epsilon_0)[/tex] into P to get E?
 
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  • #2
Why are you using the general solution of Laplace's equation in Spherical coordinates (with azimuthal symmetry), when cylindrical coordinates are more appropriate?
 
  • #3
gabbagabbahey said:
Why are you using the general solution of Laplace's equation in Spherical coordinates (with azimuthal symmetry), when cylindrical coordinates are more appropriate?

You are right. I just realized that. Is my approach to the problem correct? I should not necessarily assume that the length of a very long cylinder is approaching infinity?
 
  • #4
I would assume that the cylinder is infinitely long...Are there any symmetries present (eg. axial, radial, azimuthal etc.)? What is the general solution to Laplace's equation in cylindrical coordinates with these symmetries?
 

1. What is an electric field in a dielectric material?

An electric field in a dielectric material is a region of space where electric charges experience a force due to the presence of an electric field. Dielectric materials are insulators, meaning they do not conduct electricity, and they can become polarized when placed in an electric field.

2. What causes an electric field in a dielectric material?

An electric field in a dielectric material is caused by the presence of an external electric field. When an external electric field is applied to a dielectric material, the molecules within the material reorient and align with the field, resulting in the creation of a new electric field within the material.

3. How does a dielectric material affect the strength of an electric field?

A dielectric material can reduce the strength of an electric field by polarizing and creating an opposing electric field within the material. This results in a lower net electric field within the material, making it more difficult for charges to move through it.

4. What is the relationship between electric field and dielectric constant?

The dielectric constant, also known as the relative permittivity, is a measure of how easily a material can be polarized by an external electric field. The electric field within a dielectric material is directly proportional to its dielectric constant, meaning the higher the dielectric constant, the stronger the electric field within the material.

5. How does the presence of a dielectric material affect the capacitance of a capacitor?

The presence of a dielectric material between the plates of a capacitor increases its capacitance. This is because the polarized molecules within the dielectric material create an opposing electric field, allowing for more charge to be stored on the plates of the capacitor.

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