= Charged sheet between grounded parallel plates
{title2=$V(0)=\sigma d/(4\varepsilon_0)$}
Place an infinite sheet of <surface charge density> $\sigma$ at $z=0$ between grounded conducting planes $z=\pm d/2$, in <vacuum>. Reflection symmetry and <Gauss's law> give $E_z=\sigma\operatorname{sgn}(z)/(2\varepsilon_0)$ in the two gaps. Integrating the <electric field> with zero <electric potential> at the conductors gives $V(z)=\sigma(d/2-|z|)/(2\varepsilon_0)$. Each facing conducting surface carries induced <surface charge density> $-\sigma/2$. For $\sigma>0$, an <Electron> released from rest at a plate reaches the sheet with <kinetic energy> $e\sigma d/(4\varepsilon_0)$; its nonrelativistic <speed> follows from $m_ev^2/2$.
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