Consider an infinite flat sheet with positive charge density σ in which a circular hole of radius R has been cut out. The sheet lies in the xy-plane with the origin at the center of the hole. The sheet is parallel to the ground, so that the positive z-axis describes the "upward" direction. If a particle of mass m and negative charge −q sits at rest at the center of the hole and is released, the particle, constrained to the z-axis, begins to fall. As it drops farther beneath the sheet, the upward electric force increases. For a sufficiently low value of m, the upward electrical attraction eventually exceeds the particle’s weight and the particle will slow, come to a stop, and then rise back to its original position. This sequence of events will repeat indefinitely.

Required:
a. What is the z-component of the electric field at a depth Δ beneath the origin along the negative z-axis?
b. What is the maximum mass mmax that would prevent the particle from falling indefinitely?
c. If m < mmax, hew much work is done by the Electric field the particle drops from z 0 to z = - Δ