# Interpretation of the Debye length

## Main Question or Discussion Point

What exactly is the Debye length?

From what I understand, when a charge q>0 is shielded by an electron cloud, then the Debye length is the distance the potential of the charge q falls by 1/e. Is it that simple?
Furthermore, how do you go about deriving the expression:

$$\lambda_D=\sqrt{\frac{\epsilon_0 \kappa_B T_e}{n_e e^{2}}}$$

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Physics Monkey
Homework Helper
Yes, that's right. The screened coulomb interaction represents some sort of average or mean field approximation to the induced field due to a point charge.

Are you interested in zero temperature screening in a metal or finite temperature screening in a plasma? In either case, the basic method for determing the potential is a self consistent method. The density determines the potential via Poisson's equation and the field determines the density in terms of the compressibility $$dn/d\mu$$ or the Boltzmann equation for probability, roughly speaking.

Are you interested in zero temperature screening in a metal or finite temperature screening in a plasma?
Thanks for your response and it is screening in a plasma i am interested in.

Physics Monkey