Dielectric in an electrostatic field

[Nakis]

Hi all,

I am sorry this could sound like heard many times before, but I am trying to understand this problem and found nothing in my physics books.

If I put a small dielectric (bit of paper) into an electrostatic field (for example generated by a rubbed plastic rod), the paper will be attracted. In theory, the electric field causes a polarization in the paper, which amounts to a surface charge... If the rod is positive, a negative charge will appear in the paper surface, resulting in an "upward" force. How can his force be calculated?

Furthermore, how does this work if I use two parallel conductor plates, put the paper on a plate and apply some potential? Here, ithe charges would be different on each side of the paper, so that it would never leave one surface to find some equilibrium position...

I know it's weird, but anyway thanks for any help !

-Nakis

 

[Meir Achuz]

The electric field produces an electric dipole moment in a small chunk of dielectric.
If the field is uniform (as between two parallel plates, there will be no force, as you suggested. You need a non-uniform field to get a force. For instance, the force on a dielectric sphere of radius R a distance d from a point charge q is
F=[(1-epsilon/2+epsilon)]2q^2R^3/d^5. This is in Gaussian units.
It is a bit more complicated in SI. The dielectric factor would be somewhat different
(and difficult to calculate) for other shapes