LOCAL (INTERNAL) FIELD OR LORENTZ RELATION:
Definition
When a dielectric material is subjected to an external electric field, each of the atoms develops a dipole moment and act as an electric dipole. Hence the resultant field at a given atom will be the sum of applied electric field and the electric field due to surrounding dipoles.
This resultant field acting at an atom in a dielectric is called local field (or) internal field
(Eint). This was first calculated by Lorentz.
Calculation of local field (or) internal field (Eint)
To calculate local field, consider a dielectric material and is inserted between the two conducting plates of a capacitor. An electric field ‘E’ is applied to the capacitor then the dielectric material is uniformly polarized, as a result opposite type of charges are induced on the surface of the dielectric near the capacitor plates.
Let us assume a small sphere region or cavity of radius ‘r’ around the atom A within the dielectric at which the local field is to be calculated. It is also assumed that the radius of the cavity is large compared to the radius of the atom. i.e., there are many atomic dipoles within the sphere. The total electric field acting on the central atom of the sphere is called local field (or) internal field.
Eint = E1+E2+E3+E4 (1)
where,
E1 = Field at A due to the charges on the plates (externally applied).
E2 = Field at A due to the polarized charges induced on the two sides of dielectric.
E3 = Field at A due to the polarized charges induced on the surface of the spherical cavity.
E4 = Field at A due to the atomic dipoles inside the spherical cavity.