Why does the dielectric field not cancel out the capacitor's field? When a conductor is in a region with electric field, free charges will move until they balance out the external electric field. However in dielectrics this does not happen. I know that charges are bounded to the atoms, and there is only a small portion that will be near the surface of the the capacitor, but should we not also  consider the small electric fields inside the polarized atoms? They may add up and cancel out the external field.
 A: 
why does not the dielectric field cancel out the capacitor's field?

The polarization of the dielectric in the capacitor does reduce the effective electric field of the capacitor, but doesn't completely cancel it out. The reason is the molecules of the dielectric material are not perfectly polarized by the capacitor's electric field.
See the diagrams below taken from the following link on the Hyperphysics website: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html
Note that the polarization of the dielectric by the capacitor's electric field does not result in perfect alignment of the dipoles with the electric field. The greater the dielectric constant $k$ of the dielectric, the better the alignment and cancelling effect. The effective electric field is then
$$E_{effective}=E-E_{polarization}=\frac{σ}{kε_0}$$
Where $σ$= charged density = $\frac{Q}{A}$
$ε_0$ = permittivity of free space.
Hope this helps.

A: The charges in the dielectric to rearrange and lessen the field inside of the capacitor, the field just isn't completely canceled. This is because, as you said, we are dealing with bound charges.
If you compare a vacuum filled capacitor with charge $\pm Q$ on its plates to a capacitor with the same charge filled with a linear dielectric of dielectric constant $k$, you will find the field inside the second capacitor to be
$$E_\text{eff}=E_0-E_\text{polarization}=\frac 1k\cdot E_0$$
The field will only be canceled when $k\to\infty$, which is true for conductors, as you seem to be aware of already.
A: Any volume element within the dielectric that's large enough to encompass many molecules, but smaller than any scale of interest, will be electrically neutral regardless of whether or not there is an induced polarization. So the molecules in the bulk do not contribute to the macroscopic electric field.
