Definition:Macroscopic Electric Field
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Definition
Consider a volume element $\delta V$ of $B$ which is much bigger than a single atom, but still small compared to the volume of $B$.
The macroscopic electric field is the mean atomic electric field over $\delta V$.
Motivation
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.
Also see
- Results about macroscopic electric fields can be found here.
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 macroscopic electric field