Finding volume and surface densities of bound charge

In summary, a slab of material with parallel faces (one at z = 0 and the other at z = zt) has a non-uniform polarization P = P(1 + αz)zˆ, where P and α are constants. The volume density of bound charges can be found by integrating the local surface density of bound charge, which is given by ##\vec P. \hat n ##. The local volume density of surface charge is ##- \vec \nabla.\vec P ##, which can be integrated over the whole volume to find the total bound volume charge.
  • #1
Askhat15
1
0

Homework Statement


A slab of material has parallel faces. One coincides with the xy plane (z = 0), while the other is given by z = zt . The material has a nonuniform polarization P = P(1 + αz)zˆ where P and α are constants. Fin the volume and surface densities of bound charges[/B]

The Attempt at a Solution


I think that
cramster-equation-20101110855506342497615036712447177.gif
holds for this case. However, I couldn't any further. Please, help asap. Will appreciate so much![/B]
 
Physics news on Phys.org
  • #2
Locally the surface density of bound charge is ##\vec P. \hat n ##. Here ##\vec P## is polarization and ##\hat n## is the unit vector along the direction of local surface area. Now integrate it over the whole surface to get the total bound surface charge. Similarly the local volume density of surface charge is ##- \vec \nabla.\vec P ##. Integrate it over the whole volume to get the total bound volume charge.
 

Related to Finding volume and surface densities of bound charge

1. What is the difference between volume density and surface density?

Volume density refers to the amount of bound charge per unit volume, while surface density refers to the amount of bound charge per unit area of a surface. In other words, volume density is a measure of how tightly packed the bound charge is within a certain volume, while surface density is a measure of how concentrated the bound charge is on a surface.

2. How do you find the volume density of bound charge?

To find the volume density of bound charge, you must first calculate the total amount of bound charge within the given volume. This can be done by integrating the charge density over the volume. Then, divide this total charge by the volume to get the volume density.

3. What is the formula for surface density of bound charge?

The formula for surface density of bound charge is simply the amount of bound charge divided by the surface area. This can also be written as the surface integral of the charge density over the surface area.

4. How does the bound charge affect electric fields?

Bound charge creates an electric field that is opposite in direction to the external electric field. This means that the presence of bound charge can weaken or cancel out the effects of the external electric field in the region where it is present.

5. Can you have negative bound charge?

Yes, bound charge can be either positive or negative. Positive bound charge is caused by an excess of protons in an atom, while negative bound charge is caused by an excess of electrons. Both types of bound charge can affect the electric field in different ways.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
932
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
768
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
9K
  • Advanced Physics Homework Help
Replies
2
Views
4K
Back
Top