Show that the D field due to a point charge has a divergence of zero

A point charge, q = -5.0 nC, and m = 2.0 x 10-18 kg, is shot vertically upward with an initial speed of 3.0 x 105 m/s from a thin, infinite, planar sheet of uniform charge with surface charge density of σ = +4.0 nC/m^2 . To what vertical elevation will q rise above the sheet of charge? Neglect gravity

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Four equal charges, q, are fixed at the corners of a square of side a in the xy-plane centered on the origin. A bead of mass m and charge -q is positioned at the origin. A thin, frictionless string along the z-axis threads the bead, thus restricting its mo- tion to the z-axis. The bead is then displaced from the origin by a small amount Zo < 0 and released from rest. Show that the bead undergoes simple harmonic motion (to a very good approximation), and derive an expression for its period of oscillation in terms of known parameters.