In electricity (electromagnetism), the electric susceptibility (; Latin: susceptibilis "receptive") is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field. The greater the electric susceptibility, the greater the ability of a material to polarize in response to the field, and thereby reduce the total electric field inside the material(and store energy). It is in this way that the electric susceptibility influences the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light. Definition for linear dielectrics If a dielectric material is a linear dielectric, then electric susceptibility is defined as the constant of proportionality (which may be a matrix) relating an electric field E to the induced dielectric polarization density P such that where is the polarization density; is the electric permittivity of free space (electric constant); is the electric susceptibility; is the electric field. In materials where susceptibility is anisotropic (different depending on direction), susceptibility is represented as a matrix known as the susceptibility tensor. Many linear dielectrics are isotropic, but it is possible nevertheless for a material to display behavior that is both linear and anisotropic, or for a material to be non-linear but isotropic. Anisotropic but linear susceptibility is common in many crystals. The susceptibility is related to its relative permittivity (dielectric constant) by so in the case of a vacuum, At the same time, the electric displacement D is related to the polarization density P by the following relation: where Molecular polarizability A similar parameter exists to relate the magnitude of the induced dipole moment p of an individual molecule to the local electric field E that induced the dipole. This parameter is the molecular polarizability (α), and the dipole moment resulting from the local electric field Elocal is given by: This introduces a complication however, as locally the field can differ significantly from the overall applied field. We have: where P is the polarization per unit volume, and N is the number of molecules per unit volume contributing to the polarization. Thus, if the local electric field is parallel to the ambient electric field, we have: Thus only if the local field equals the ambient field can we write: Otherwise, one should find a relation between the local and the macroscopic field. In some materials, the Clausius–Mossotti relation holds