Space-charge-filled parallel-plate capacitor
= Space-charge-filled parallel-plate capacitor
{title2=$V''=-\rho/\epsilon_0$}
Between large plates at prescribed <electric potentials> and separation $d$, fixed uniform <charge density> $\rho$ gives $V(x)=V_1+(V_2-V_1)x/d+\rho x(d-x)/(2\epsilon_0)$ by <Poisson's equation>. The signed <electric field> is linear. Its magnitude can have an interior V-shaped minimum, so a sketch of signed field alone need not answer a request for field magnitude.