Surface Integral: field intensity at center of cavity in

[spencer]

So this is technically an electromagnetics problem, but I think if I explain the mathematical implications of the problem, it should be strictly math.

Problem:
Determine the electric field intensity at the center of a small spherical cavity cut out of a large block of dielectric in which a polarization P exists.

In math terms:
A sphere is distributed with charge such that the highest concentration of negative charges is at the top and the highest concentration of positive charges is at the bottom. Describe the charge density mathematically.

Implications:
So what we're dealing with is a distribution over the surface of a sphere that changes in some sinusoidal way (negative charge-->neutral charge-->positive charge-->neutral charge-->repeat). I'm trying to set up a surface integral over the sphere - any thoughts?

Thanks a ton,
Spencer

 

[Deleted member 4993]

Re: Help setting up Surface Integral

So this is technically an electromagnetics problem, but I think if I explain the mathematical implications of the problem, it should be strictly math.

Problem:
Determine the electric field intensity at the center of a small spherical cavity cut out of a large block of dielectric in which a polarization P exists.

In math terms:
A sphere is distributed with charge such that the highest concentration of negative charges is at the top and the highest concentration of positive charges is at the bottom. Describe the charge density mathematically.

Implications:
So what we're dealing with is a distribution over the surface of a sphere that changes in some sinusoidal way (negative charge-->neutral charge-->positive charge-->neutral charge-->repeat). I'm trying to set up a surface integral over the sphere - any thoughts?

Thanks a ton,
Spencer

Why sininusoidal distribution - is it given?

Why not think about the charge distribution as spherical - where the center of the "charge distribution" sphere is slightly shifted from the center?

You'll get this type of distribution - if you bring another charged particle near (but sufficiently away to avoid local perturbation)) to the charged sphere.

 

[spencer]

Re: Help setting up Surface Integral

I said sinusoidal, because my professor suggested it. How does considering an off-center charge work out integral-wise? I'm sorry if this seems trivial - I haven't dealt with a non-uniform charge distribution before.