Electric Field of a Polarized Electret

[xxbigelxx]

1. The problem statement, all variables and given/known data
An elecret is a dielectric that has a quasi-permanent polarization when there is no applied field. Consider a uniformly polarized cylindrical electret. The cylinder has a radius of 10h and a length h. The polarization is Pk where k is a unit vector along the axis.

a. Draw the electric field lines.
b. Calculate the electric field at the center of the cylinder. Ignore edge effects.
c. Calculate the electric field on the midplane of the cylinder at a distance
100h from the center. The approximation of a point dipole can be used since the distance is very large.


2. Relevant equations



3. The attempt at a solution
I need help with pretty much all of this problem. I am unsure of which formulas to use, as well as drawing the field lines. Would the field lines just be from the bottom of the cylinder to the top of it? Thanks.

[gabbagabbahey]

1. The problem statement, all variables and given/known data
An elecret is a dielectric that has a quasi-permanent polarization when there is no applied field. Consider a uniformly polarized cylindrical electret. The cylinder has a radius of 10h and a length h. The polarization is Pk where k is a unit vector along the axis.

a. Draw the electric field lines.
b. Calculate the electric field at the center of the cylinder. Ignore edge effects.
c. Calculate the electric field on the midplane of the cylinder at a distance
100h from the center. The approximation of a point dipole can be used since the distance is very large.


2. Relevant equations



3. The attempt at a solution
I need help with pretty much all of this problem. I am unsure of which formulas to use, as well as drawing the field lines. Would the field lines just be from the bottom of the cylinder to the top of it? Thanks.

Well, field lines always go from positive charges to negative charges, right? So the first step is to figure out how the bound charge is distributed....how are bound surface and volume charge densities related to polarization?

[xxbigelxx]

I think I made some progress here. I have the E lines going from the top to the bottom.
My only question remaining is for part c. Does the midplane mean above the cylinder, or to the side of it? I calculated the distance as if its 100h above the cylinder, along the axis.

[gabbagabbahey]

Does the midplane mean above the cylinder, or to the side of it? I calculated the distance as if its 100h above the cylinder, along the axis.

The midplane is the plane orthogonal to the axis of the cylinder, passign through its center. So, if your cylinder is centered on the origin (going from z=-h/2 to z=+h/2), a point in its midplane 100h from the center would be at r=100h, z=0 in cylindrical coordinates.

[xxbigelxx]

So I would use this equation with a theta value of 90?