Effective permittivity and permeability  Effective permittivity and permeability are averaged dielectric and magnetic characteristics of a microinhomogeneous medium. They are subject of Effective medium theory . There are two widely used formulae . They both were derived in quasi-static approximation when electric field inside a mixture particle may be considered as homogeneous. So, these formulae can not describe the particle size effect. Many attempts were undertaken to improve these formulae. The first formula was proposed by J.C. Maxwell Garnett . Maxwell Garnett was the son of physicist William Garnett, and was named after Garnett's friend, James Clerk Maxwell. He proposed his formula to explain colored pictures that are observed in glasses doped with metal nanoparticles. His formula has a form  formula_1 (1)  where formula_2 is effective relative complex permittivity of the mixture, formula_3 is relative complex permittivity of the background medium containing small spherical inclusions of relative permittivity formula_4 with volume fraction of formula_5. This formula is based on the equality  formula_6 (2)  where formula_7 is the absolute permittivity of free space and formula_8 is electric dipole moment of a single inclusion induced by the external electric field . However this equality is good only for homogeneous medium and formula_9. Moreover the formula (1) ignores the interaction between single inclusions. Because of these circumstances, formula (1) gives too narrow and too high resonant curve for plasmon excitations in metal nanoparticles of the mixture . The second popular formula was proposed by D.A.G. Bruggeman . His formula has a form  formula_10 formula_11 (3)  Here positive sign before the square root must be altered to negative sign in some cases in order to get correct imaginary part of effective complex permittivity which is related with electromagnetic wave attenuation. This formula is based on the equality  formula_12 (4)  where formula_13 is the jump of electric displacement flux all over the integration surface, formula_14 is the component of microscopic electric field normal to the integration surface, formula_15 is the local relative complex permittivity which takes the value formula_4 inside the picked metal particle, the value formula_3 inside the picked dielectric particle and the value formula_2 outside the picked particle, formula_19 is the normal component of the macroscopic electric field. Formula (4) comes out of Maxwell's equality formula_20.