Distribution of Macroscopic Electric Charge within Insulator
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Theorem
Let $B$ be a body made out of an electrically insulating substance.
Then it is possible for different volume elements of $B$ to have different (macroscopic) electric fields caused by intrinsic imbalance of the electric charges distributed throughout $B$.
Proof
In an electrical insulator, electric charges cannot flow, because of the nature of the substance.
Hence an electric charge in one point within $B$ cannot flow to another point within $B$ under a potential difference caused by the presence of those (macroscopic) electric fields.
$\blacksquare$
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