Polarization of a solid sphere of nonconducting material

In summary: Plugging in 2a for R is the correct way to solve the problem. Nonconducting materials do not affect the validity of Gauss' law.
  • #1
goohu
54
3
Homework Statement
see picture
Relevant Equations
1) surface charge density = P * an
2) volume charge density = -\nabla \cdot P
3) Gauss law for polarization
a) Just using the equations gives us:
surface charge density = ## \rho_{\rho s} = kR^2 ##
volume charge density = ## \rho_\rho = -4kR ##

b) I am not sure here but the Q on the shell is the same as within. If that's the case we can use gauss law to find Q which I guess is the total charge.

## -Q = \int \rho_{\rho s} \cdot ds ##

My textbook states (for conductors) any introduced charge will move to the surface and redistribute itself due to repulsion. In this case the total charge on the shell is the same as "within"?

c) The E-field can also be found form gauss law. Then I assume you plug in 2a as R? This would be the standard way of solving the problem but IDK if nonconducting material is a special case?
 

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  • #2
goohu said:
a) Just using the equations gives us:
surface charge density = ## \rho_{\rho s} = kR^2 ##
What is the value of ##R## at the surface?

volume charge density = ## \rho_\rho = -4kR ##
Looks good.

b) I am not sure here but the Q on the shell is the same as within. If that's the case we can use gauss law to find Q which I guess is the total charge.

## -Q = \int \rho_{\rho s} \cdot ds ##

My textbook states (for conductors) any introduced charge will move to the surface and redistribute itself due to repulsion. In this case the total charge on the shell is the same as "within"?

You should be able to calculate separately the total surface charge and the total volume charge. Then you can check to see of the total surface charge is equal and opposite to the total volume charge.

c) The E-field can also be found form gauss law. Then I assume you plug in 2a as R? This would be the standard way of solving the problem but IDK if nonconducting material is a special case?
Gauss' law is always valid.
 
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Related to Polarization of a solid sphere of nonconducting material

1. What is polarization of a solid sphere of nonconducting material?

Polarization is the process in which the electric dipole moments of atoms or molecules in a material align in a particular direction when an external electric field is applied. In a solid sphere of nonconducting material, the atoms or molecules are fixed in place, but their dipole moments can still align with the electric field, resulting in polarization.

2. How does polarization occur in a solid sphere of nonconducting material?

When an external electric field is applied to a solid sphere of nonconducting material, the positive and negative charges within the material are separated, creating an electric dipole moment. As the electric field changes direction, the dipole moments of the atoms or molecules also change direction, resulting in polarization.

3. What factors affect the degree of polarization in a solid sphere of nonconducting material?

The degree of polarization in a solid sphere of nonconducting material is affected by the strength of the external electric field, the dielectric constant of the material, and the shape and size of the sphere. Materials with higher dielectric constants and smaller spheres will generally have a higher degree of polarization.

4. How is polarization measured in a solid sphere of nonconducting material?

Polarization is typically measured by the dipole moment per unit volume, also known as the polarization density. This can be calculated by dividing the total dipole moment of the material by its volume. Another way to measure polarization is by the polarization vector, which represents the direction and magnitude of the dipole moment.

5. What are the applications of polarization in solid spheres of nonconducting material?

Polarization in solid spheres of nonconducting material has various applications, including in capacitors, dielectric materials, and optical devices. It is also used in technologies such as LCD screens, where the alignment of polarized light allows for the creation of images. In addition, polarization is important in understanding the behavior of materials in electric fields and in the study of electromagnetic waves.

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