Bjerrum length

The Bjerrum length $(l_{B})$ is the distance for which the electrostatic potential energy between two charges, $e$, is equal to the thermal energy scale $k_{B}T$. Using Coulomb's law, one sets

$k_{B}T={\frac {e^{2}}{4\pi \varepsilon _{0}\varepsilon _{r}}}{\frac {1}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}$

leading to

$l_{B}={\frac {e^{2}}{4\pi \varepsilon _{0}\varepsilon _{r}k_{B}T}}$

See also

• Debye length