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

$k_{B}T=\frac{e^2}{4\pi {\epsilon }_0{\epsilon }_r}\frac{1}{|{\mathbf{r}}_1-{\mathbf{r}}_2|}$

leading to

$l_B=\frac{e^2}{4\pi {\epsilon }_0{\epsilon }_r{k}_{B}T}$

See also

• Debye length