Bjerrum length
The Bjerrum length Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (l_B)} is the distance for which the electrostatic potential energy between two charges, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e} , is equal to the thermal energy scale Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_BT} . Using Coulomb's law, one sets
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_BT = \frac{e^2}{4\pi\varepsilon_0 \varepsilon_r} \frac{1}{|\mathbf{r}_1 - \mathbf{r}_2|}}
leading to
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle l_{B}={\frac {e^{2}}{4\pi \varepsilon _{0}\varepsilon _{r}k_{B}T}}}