Debye length

In plasmas and electrolytes the Debye length (also called Debye radius), named after the Dutch physicist and physical chemist Peter Debye, is the measure of a charge carrier's net electrostatic effect in solution, and how far those electrostatic effects persist. A Debye sphere is a volume whose radius is the Debye length. With each Debye length, charges are increasingly electrically screened. Every Debye‐length, the electric potential will decrease in magnitude by 1/e. The notion of Debye length plays an important role in plasma physics, electrolytes and colloids (DLVO theory).

The Debye length arises naturally in the thermodynamic description of large systems of mobile charges. In a system of ${\displaystyle N}$ different species of charges, the ${\displaystyle j}$-th species carries charge ${\displaystyle q_{j}}$ and has concentration ${\displaystyle n_{j}(\mathbf {r} )}$ at position ${\displaystyle \mathbf {r} }$. According to the so-called "primitive model", these charges are distributed in a continuous medium that is characterized only by its relative static permittivity, ${\displaystyle \varepsilon _{r}}$. This distribution of charges within this medium gives rise to an electric potential ${\displaystyle \Phi (\mathbf {r} )}$ that satisfies Poisson's equation:

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