The wake potential associated with the passage of swift protons through a solid material using cylindrical coordinates is studied. Full results of the wake potential as a function of space when a proton moves parallel with and perpendicular to the surface are presented. Three different points are approach: (i) Dielectric analysis based on the damping, velocity and kind of material (ii) The influence of a damping on the wake potential and induced forces (stopping and lateral) (iii) The coordinates of the internal.