diff --git a/src/3_drude_model.md b/src/3_drude_model.md index ac49dbb66f0c5b5858d144bc55bad758753d6ddd..02661e0fcea01731f60e22a1902409f72efbc5e2 100644 --- a/src/3_drude_model.md +++ b/src/3_drude_model.md @@ -149,7 +149,7 @@ m⟨\mathbf{v}(t+dt)⟩ &= [m⟨\mathbf{v}(t)⟩ - e (\mathbf{E} + \mathbf{v} × &\quad\quad\quad\quad + e (\mathbf{E} + \mathbf{v} × \mathbf{B}) m⟨\mathbf{v}(t)⟩dt²/τ. \end{align} $$ -We now neglect the term proportional to $dt²$ (it vanishes when $dt → ∞$). +We now neglect the term proportional to $dt²$ (it vanishes when $dt → 0$). Finally, we recognize that $(⟨\mathbf{v}(t+dt)⟩ - (⟨\mathbf{v}(t)⟩)/dt = d⟨\mathbf{v}(t)⟩)/dt$, and arrive to $$ m\frac{d⟨\mathbf{v}⟩}{dt} = -m\frac{⟨\mathbf{v}⟩}{τ} -e\left(\mathbf{E}+⟨\mathbf{v}⟩×\mathbf{B}\right).