Definition:Macroscopic Electric Field/Motivation

Motivation behind Definition of Macroscopic Electric Field

The atomic electric field within a body of matter is not very useful to make use of in practice.

This is because, while it is possible to understand its qualitative features, it is not possible to know the atomic charge density $\rho_{\text {atomic} }$.

Not only does $\rho_{\text {atomic} }$ vary continuously within an atom, but the atoms themselves are in constant motion.

Hence the macroscopic electric field is introduced which smooths out the fine detail and presents it as an average.

Sources

• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.3$ Electric Fields in Matter: $1.3.3$ The macroscopicelectric field