Prove that uniformly charged grid filaments with square cells focus a parallel electron beam that has passed through the cell to a point if the thickness of the filaments is much smaller than the cell size and the beam falls perpendicular to the grid plane. What is the focal length of such a cell if the electric field away from the grid plane is uniform and on the right is E₁, on the left is E₂, and the electron energy is eV₀?
7.3 Motion in an alternating electric field