Two main avenues leading to the Maxwell Garnett mixing rule

This article discusses the basic form of Maxwell Garnett mixing formula, in other words the prediction for the effective permittivity of a dielectric mixture with spherical scatterers in a homogeneous environment. In particular, the analysis focuses on the different ways to arrive at the mixing rule result. Two main lines of derivation are discussed: the physics-based polarizability approach and the more engineering-oriented averaging approach. Two different principles for the latter approach are given: averaging both using fields and energy densities. The article argues for the natural character and persuasiveness of the Maxwell Garnett mixing rule, not least because the analyses require astonishingly few ad hoc assumptions.