A surprisingly realistic microscopic model for the charge density of a semi-infinite metal (with z = 0 as its macroscopic surface) consists of a positive charge distribution

And a negative charge distribution:

(a) Sketch n+(z) and n−(z) on the same graph and give a physical explanation of why they might be reasonable.
(b) Calculate the dipole moment p per unit area of surface for this system.
(c) Calculate the electrostatic potential φ(z) and sketch it in the interval −∞ (d) Calculate and explain the value of φ(∞) − φ(−∞).
(d) Calculate the total electrostatic energy per unit area of this system.

n+(z) = { 0 Z < 0, Z > 0,