Electrostatic deflection by finite parallel plates ($x=V_d\ell D/(2d{U}_a)$)

An electron accelerated through voltage $U_a$ crosses deflecting plates of length $\ell$ and separation $d$. If their electric field is uniform and their centre is distance $D$ from a screen, constant transverse acceleration inside the plates followed by free drift gives the displayed screen displacement. It includes the displacement accumulated inside the plates. The plate-exit displacement is $x\ell /(2D)$, which must be smaller than the half-gap for a centrally injected beam to pass.