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

 

[Graeme Robinson]

Hello Nakis,

Great question! Dielectrics in an electrostatic field can be a bit tricky to understand, but I'll do my best to explain it.

First, let's define what a dielectric is. A dielectric is a material that does not conduct electricity, such as paper. When a dielectric is placed in an electrostatic field, the electric field causes the molecules in the dielectric to become polarized. This means that the positive and negative charges within the molecules become separated, with the positive charges aligning towards the negative charge and vice versa. This creates a net dipole moment in the dielectric.

Now, when you bring a positively charged object, such as a rubbed plastic rod, near the dielectric, the positive charges in the dielectric will be attracted to the negative charge on the rod, causing the dielectric to be attracted to the rod. This is because opposite charges attract each other.

To calculate the force on the dielectric, we can use the equation F = qE, where F is the force, q is the charge, and E is the electric field strength. In this case, the charge is the induced charge on the surface of the dielectric, and the electric field strength is the electric field from the charged object. So, the force on the dielectric can be calculated by multiplying the induced charge by the electric field strength.

Now, for your second question about using two parallel conductor plates with the dielectric in between. In this case, the dielectric will still be attracted to the positively charged plate, but it will also be repelled by the negatively charged plate. This creates a net force on the dielectric, causing it to move towards the positively charged plate. However, once it reaches the plate, the charges on either side of the dielectric will balance out, resulting in an equilibrium position where the dielectric is neither attracted nor repelled by either plate.

I hope this helps clarify things for you. Let me know if you have any other questions!