Final answer:
The local field in a dielectric medium, El, is the sum of the external electric field and the induced electric field inside the dielectric. El is related to the dielectric constant εr and the external electric field E by the equation El = E(εr + 2/3), where εr is the ratio of Eo to E.
Step-by-step explanation:
The local field in a dielectric medium conceptually represents the actual electric field experienced by the individual molecules within the dielectric material, which is different from the externally applied electric field E. This is due to the fact that the presence of the dielectric leads to an induced electric field Ei which opposes the original field. Consequently, the local field El is the sum of the external electric field and the induced electric field.
When a dielectric is placed in an external electric field, polar molecules within the dielectric align with the field, inducing surface charges which create an opposing induced electric field Ei. The relation between the local field El, the external electric field E, and the relative permittivity (dielectric constant) εr is given by El = E(εr + 2/3).
The dielectric constant εr is the ratio of the electric field without the dielectric (Eo) to the net electric field within the dielectric (E). The induced charges on the surface of the dielectric result in an induced field that partially cancels the external field, reducing its overall strength within the dielectric material. This effect is quantified by the dielectric constant, which is always greater than one for a dielectric material, indicating the reduction in electric field strength due to the dielectric.