## How Dielectrics Work

Each material is made up of atoms. Each atom consists of a cloud of electrons surrounding a positively charged central nucleus.When no electric field is applied the electron cloud exhibits spherical symmetry as shown in the diagram. In the presence of an electric field the charge cloud is distorted. The electrons – being negatively charged - are displaced in in a direction opposite to the direction of the applied electric field – as in the diagram below. This can be reduced to a simple dipole by finding the distance between the centres of positive and negative charge. The effect is that the microscopic electric field is reduced by where is the charge on an electron and is the distance between the centres of the charges.. When we multiply this by the number of atoms per unit volume we find the charge in the rectangle drawn around each plate is reduced to where is the induced charge per unit area of the capacitor plate. Applying Gauss's Divergence Theorem,    Put to get  