diff options
Diffstat (limited to 'content/know/concept/boltzmann-relation')
| -rw-r--r-- | content/know/concept/boltzmann-relation/index.pdc | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/content/know/concept/boltzmann-relation/index.pdc b/content/know/concept/boltzmann-relation/index.pdc index ddaa22f..b892745 100644 --- a/content/know/concept/boltzmann-relation/index.pdc +++ b/content/know/concept/boltzmann-relation/index.pdc @@ -39,16 +39,16 @@ $$\begin{aligned} = - k_B T_e \nabla n_e \end{aligned}$$ -At equilibrium, we demand that $\vb{f}_e = \vb{f}_p$, +At equilibrium, we demand that $\vb{f}_e = - \vb{f}_p$, and isolate this equation for $\nabla n_e$, yielding: $$\begin{aligned} k_B T_e \nabla n_e - = q_e n_e \nabla \phi + = - q_e n_e \nabla \phi \quad \implies \quad \nabla n_e - = \frac{q_e \nabla \phi}{k_B T_e} n_e - = \nabla \bigg( \frac{q_e \phi}{k_B T_e} \bigg) n_e + = - \frac{q_e \nabla \phi}{k_B T_e} n_e + = - \nabla \bigg( \frac{q_e \phi}{k_B T_e} \bigg) n_e \end{aligned}$$ This equation is straightforward to integrate, |