An uncharged parallel-plate capacitor with spacing d is horizontal. A small bead with mass m and positive charge q is shot straight up from the bottom plate with speed v₀. It reaches maximum height y_max before falling back. Then the capacitor is charged with the bottom plate negative. Find an expression for the capacitor voltage ΔV_C for which the bead’s maximum height is reduced to 1/2y_max. Ignore air resistance.