Lecture #8 Electric dipoles. Dielectrics. Electric Capacitance and Capacitors

is appropriate only
when there is a vacuum between the capacitor plates

Dielectric inside capacitor

When a nonconducting (electrically insulating) material is inserted between the plates, the capacitance increases, even though the area and separation remain constant. The ratio of the new capacitance to the capacitance in a vacuum is called the dielectric constant
(Greek letter kappa):
Materials that do not conduct
electric charge are also
known as dielectrics

(c) The net field between the plates is reduced, leading increased capacitance.

Dielectric inside capacitor
(a) The field of a parallel-plate capacitor without any material between the plates, (b) An induced charge on the surfaces of an insulating material placed between plates generates a field within the material opposite in direction to the original field,

Two oppositely charged parallel plates form a capacitor. Capacitor depends on the area of the plates, the dielectric constant of the insulating material, and the thickness of the dielectric layer.

The Parallel-Plate Capacitor

The electric field due to a pair of oppositely charged parallel plates is uniform except near the edges, (a) Schematic representation of the field, (b) Field lines as indicated by small threads suspended in oil between oppositely charged plates

Electric Field of a Parallel-Plate Capacitor
A cylindrical Gaussian surface oriented with its axis perpendicular to two parallel charged plates . One end of the Gaussian surface is inside the metal plate.
Electric Field of a Parallel-Plate Capacitor
According to Gauss's law, the flux is proportional to the charge enclosed by the cylinder.
For this alignment there is no flux through the curved side of the cylinder. Thus all the flux must emerge through the end of area The statement of Gauss's law becomes
Where A1 is the area of the end of the cylinder, ql is the charge within, and εo is the proportionality constant (permittivity of free space).
For a flat plate we expect the charge to be uniformly distributed over the surface.
In that case the ratio of charge to area is constant and can be taken as equal to the total charge q on the plate divided by its total surface area A.