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Volume Charge Density and Non-Uniform Polarization

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Obtain an expression for the volume charge density ρ(r) associated with a non-uniform polarization P(r) in a dielectric material.

The polarization in a spherical region of radius a is:
P(r) = (P0)r(a-r)R, where P0 is a constant and R is a unit vector in the outward direction from the center of the sphere.

The sphere has no free charge and is placed in a region in which there is no externally applied electric field. Find the surface and volume charge densities on and within the sphere. Deduce the electric field E(r) within the sphere (in spherical coordinates div(F) = (1/(r^2))(d/dr)((r^2)Fr) + derivatives with respect to theta and phi).

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The polarization can be related to the volume density by:

The polarization volume density is equal to the ...

Solution Summary

This solution computes an expression for a volume charge density in a dielectric material.

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Polarization and bound charge

A slab of material has parallel faces, one coincides with the xy plane while the other is given by z=t
The material has non-uniform polarization P = P(1+a*z) in the z direction.
Find teh volume and surface bound charge densities. Find the total bound charge in a cylinder of teh material of cross section A and sides parallel to the z-axis.

see attached file.

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