How Do Dielectrics Affect Electrostatic Potential Between Conductive Bars?

[Luchopas]

Homework Statement

I have the following problem regarding to dielectric and potencial

Problem:

Consider 2 conductive bars parallel with a distance “d” between them (smal distance compared to the size of the bars), connected to diference of potencial Vo.The space between the bars is filed with a constant dielectric material epsilon = epsilon (z), in the way that epsilon(0)=epsilon 1. The electrostatic potencial between the 2 bars is :

http://img22.imageshack.us/img22/3595/formula1m.png

where K is a constant that is determined experiamentally.

Determine the following:

1) The electrostatic potencial V(z) in the region between the bars.
2) the dependence of the constant dielectric of the variable z , to be consistent with (*)
3) The free density charge of the conductors
4) The vector of polarization P and the polarization charges of the dielectric.

 

[NateD]

Homework EquationsI have the formula of the electrostatic potencial (in the statement) and the relation between the dielectric constant and the electrostatic potencial:http://img220.imageshack.us/img220/8586/formula2d.png The Attempt at a Solution1) The electrostatic potencial V(z) in the region between the bars is given by the formula in the statement:V(z)=Vo*[(1-exp(-Kz))/(1+exp(-Kz))] 2) The dependence of the constant dielectric with the variable z is determined from the relation between the dielectric constant and the electrostatic potencial:epsilon(z)=epsilon1*[1-(V(z)/Vo)]3) The free density charge of the conductors can be determined from the Gauss Law:http://img845.imageshack.us/img845/2568/formula3b.png where sigma(z) is the surface charge density in the region between the bars. 4) The vector of polarization P and the polarization charges of the dielectric can be calculated using the relation:http://img846.imageshack.us/img846/6999/formula4p.png