My basic understanding of a dielectric material is that the coulomb force between charges in a dielectric must be reduced by some factor since some of the electric field energy gets stored in the medium. The following thought experiment is confusing me and I am wondering where my mistake lies.
Lets consider the border area between two different dielectrics. Now consider a rectangular path where two opposing sides are each in a different dielectric. All sides are short enough that any E field would be constant if it were the same medium and the sides travellng through the border are very short compared to the others.
Now the work done by the E field along this path must be zero. This seems to imply that the component of the E field along the path is equal in the different dielectrics. But arent all components of the E field in the dielectric smaller by some factor?