Debye Length

#Physics

Topics

$\displaystyle \lambda_{D}=\sqrt{ \frac{D{\varepsilon}{0}k{B}T}{2z^{2}e^{2}c_{\infty}}}$

  • Is the distance at which in a model of charge screening that assumes exponential decay with respect to distance from the charge object of positive/negative ion concentrations surrounding the charge object, the charge density returns back to what it is at infinity
  • $\displaystyle D$ is the dielectric constant of the medium
  • $\displaystyle z$ is the $\displaystyle \frac{Q}{e}$ for each ion, or the charge number of the ion
  • $\displaystyle c_{\infty}$ is the concentration of the positive and negative ions at infinity relative to the charged object
  • $\displaystyle e$ is the elementary charge

$\displaystyle \lambda_{D}=\sqrt{ \frac{3D{\varepsilon}{0}k{B}T}{z^{2}e^{2}c_{\infty}}}$

  • Assumes uniform positive/negative ion charge density with respect to distance until a sudden cutoff