Unconstant permitivity between two charges

[brandon.irwin]

Unconstant permittivity between two charges

Is the dielectric constant used in the force equations for two charges an average of the dielectric constant between the charges?

What dielectric constant would be used in the equations if the dielectric constant changes over the volume between the charges?

For instance, what if an infinite sheet of plastic with some thickness (less than the distance between the charges) was placed between two charges in an infinite volume of water?

I doubt it's simply the average over the distance because I would think some field lines would be "lost" in the plastic.

 

[Integral]

You can cast the basic equation with a Permeability which varies with position. Then given a function which gives the value at each position you can use integration to get the final result. If there is a well defined boundary you can break the problem into pieces over each region. You will need to match boundary values where the medias meet.

 

[brandon.irwin]

hrmm...I don't I understand how the integral would be applied :-\

For a constant permeability, wouldn't the integral go to infinity since each step would be a constant value? Otherwise, wouldn't it just be taking the average over a distance?

I don't think I get it

 

[brandon.irwin]

bump

 

[ehild]

Is the dielectric constant used in the force equations for two charges an average of the dielectric constant between the charges?

What dielectric constant would be used in the equations if the dielectric constant changes over the volume between the charges?

For instance, what if an infinite sheet of plastic with some thickness (less than the distance between the charges) was placed between two charges in an infinite volume of water?

I doubt it's simply the average over the distance because I would think some field lines would be "lost" in the plastic.

You are right, it will not be the average. The problem of calculating the electric field around point charges in media with changing dielectric constant is very complicated except for some very symmetrical problems. You know, the electric field induces dipoles in the insulators, they arrange themselves into dipole chains, and some of the electric field lines "are lost" in this way. On the other hand, the terminals of the dipole chains at the surface of the dielectric body behave as surface charges. The field of these charges contributes to the field of the free charges outside the insulator. You certainly know that in the presence of dielectric bodies you have the vector of electric displacement D whose divergence is equal to the density of free charges. The relation between the electric field intensity E and the vector of electric displacement D is $$\B{D} =\epsilon\B{E}$$, ($$[\epsilon$$ is called the dielectric constant or the permittivity of the medium.) At the boundary between two different dielectrics the normal component of the electric displacement is the same at both sides of the boundary, and so are the tangential components of the electric field. It is the number of lines of the electric displacement which are not "lost" at the boundary, but they change direction like the light beam at refraction across the boundary between two media.

ehild