diff --git a/concepts/advanced/uniform-e-field-hj.tex b/concepts/advanced/uniform-e-field-hj.tex
index 1759188..4a17423 100644
--- a/concepts/advanced/uniform-e-field-hj.tex
+++ b/concepts/advanced/uniform-e-field-hj.tex
@@ -1,6 +1,6 @@
 \subsection{Charged Particle in Uniform Electric Field}
 
-This subsection solves the Hamilton--Jacobi equation for a charged particle in a uniform electric field, showing that Jacobi's theorem reproduces the parabolic motion dictated by the constant electric force $\vec{F} = q\vec{E}$.
+This subsection solves the Hamilton--Jacobi equation for a charged particle in a uniform electric field, showing that Jacobi's theorem reproduces the parabolic motion dictated by the constant electric force $\vec{F} = q\vec{E}$. The problem is formally identical to the projectile motion treatment in~A.06: the separation ansatz, the characteristic function, and the Jacobi inversion follow exactly the same algebra, with the gravitational acceleration $g$ replaced by $-qE_0/m$. Likewise, the uniform field between parallel plates studied in Unit~9 (e9-3) produces a constant electric force that accelerates the particle uniformly; the HJ solution presented here applies directly to that configuration as well.
 
 \dfn{Hamiltonian for a charged particle in a uniform electric field}{
 A particle of mass $m$ and charge $q$ in a uniform electric field $\vec{E} = E_0\,\hat{\bm{z}}$ (with $\vec{B} = 0$) is described by the scalar potential $\varphi = -E_0 z$ and zero vector potential. The Hamiltonian is