# Insulators

As we mentioned in the previous chapter, an insulator placed inside an electric field develops layers of positive and negative charges, as shown. These charges in turn create their own electric field (a counterfield) which points in the opposite direction (from positive to negative charge), and is weaker than the original. This partially cancels the original field, so that the net electric field inside the insulator points in the same direction as the original field, but is smaller. If $$E_{out}$$ is the field outside the insulator, the field inside is $$E_{in}=\frac1{\kappa}E_{out}$$ where $$\kappa$$ is called the dielectric constant of the insulator.
 Vacuum $$\kappa=1$$ Air $$\kappa=1.00054$$ Paper $$\kappa=3.5$$ Pure water $$\kappa=80$$

The dielectric constant is always greater than (or equal to) 1, is dimensionless, and is a property of the insulating material, not its size or shape. For example, paper has a dielectric constant of $$\kappa=3.5$$, which means that when paper is placed in an electric field, the field inside the paper is less than a third ($$\frac1{3.5}=29\%$$) of what it would be if the paper weren't there.

Find the net electric field inside this particular insulator.
How large is the counterfield?
It is a frequent mistake to confuse the counterfield with the net electric field inside the insulator.

The easier a material is to polarize, the stronger the counterfield it creates, and the larger its dielectric constant. For example, water molecules are naturally polarized, as shown in the figure. When a water molecule is placed in an electric field, it doesn't have to stretch the way atoms do: it only has to rotate to align itself with the field. Thus, it has a relatively large dielectric constant.

In a conductor, the atoms don't have to stretch or rotate at all for the material to polarize. Instead, as we mentioned earlier, charge carriers from throughout the material flow to the surface. The dielectric constant of a metal would have to be very large as a result, which means that the electric field inside a metal would be very small. We'll see how small in the next section.