How can sawdust do this in an electric field? I found this really weird question and I was hoping for some insight.
Suppose we have a glass plate that's filled with oil. Some sawdust is sprinkled on top, such that it floats around. It looks like this

There are 2 rings, P (positively charged) and N (negatively charged). These are turned on and now the whole thing looks like this:

My question is why does the saw dust in the outer ring turn to become radial? I think I could understand for a bar of metal floating on oil. The electric field would cause a build up of charge (such that the electric field inside the conductor is 0) and then this charge experiences a torque from the external electric field to become radial. But wood is an insulator so this can't happen?
 A: Nonconductive materials like wood can get polarized by an electric field even though they don't conduct a current. Molecules within it can be polarized by an electric field even if they aren't willing to give up their electrons, and when molecules can line up with the field, they will be at their lowest possible energy. In the case of a speck of wood, it would be at the lowest energy when the wood is aligned with the field.
A: Non metallic materials can consist of molecules that are polar in nature forming dipoles, or that can have dipoles induced by an external field. This is why insulators called dielectrics, which are polar in nature, are used in capacitors. When an electric field is applied between the capacitor plates, the dipoles line up with the field. In a capacitor, the aligning of the dipoles increases the capacitance of the capacitor. In your example the two rings, one negatively charged and one positively charged act as the plates of a capacitor and the oil/sawdust in between the rings serves as a dielectric.
In your case it is possible that the sawdust consists of polar molecules, though I am not familiar with the molecular structure of wood. But some oils, such as alcohols, esters, and triglycerides are polar in nature. If that is the case here, the application of the electric field between the inner and outer rings could cause the oil dipoles to align with the field. Since the sawdust sits on the oil molecules, the dust may also align with the field on with the oil. Its kind of like seeing iron filings line up with an applied magnetic field.
Whether it is the sawdust or the oil that has polar molecules, they will align with the field. The lower left diagram shows the dipoles randomly arranged in the absence of an applied field. The lower right shows alignment of the dipoles with the application of the field, except inside the inner ring since there would be no field there. For clarity, the dipoles are not shown superimposed on the sawdust, but the sawdust would be aligned with the dipoles, except inside the inner ring, because there is no field there.
Hope this  helps.

A: Let's generalize a little and consider these as "long particles" floating in a fluid. Now they're not conductors, but that's not actually important because we can induce a charge in them. In this case, induction is the charging of an object by bringing it close to a charged object. It can happen in any material, and essentially creates what's called an electric dipole in the material, which causes the change in orientation. 
