Q1 ) In a hollow metallic sphere with the radius r, there is a spherical homogeneous space charge distribution rotationally symmetrical around the center of the sphere with the radius N . The outer space is field-free. The following graphic should clarify the structure again. Note the symmetry in the following calculations. It helps with all calculations! No numerical solutions are expected. The permittivity of the entire space within the sphere is the same!

a) Give the electric field vector E = (Ex, Ey, Ez) in the outside area with all its three components! E= b) Determine the total charge Q,.„,„, charge as a function of the volume charge! Ctiolurne = c) Determine the charge 04,,r,„ charge of the metal ball as a function of the surface charge density of the metal ball! • = d) Now give the surface charge density pc as a function of the volume charge density p,;? Pr = e) Give the electric field E with all its components in spherical coordinates depending on the charge 0„,,m„, charge (and the radius) in the area between the volume charge and the surface charge. Note the permittivity of the material! E= f) Give the electric field E with all its components in spherical coordinates as a function of the charge Qvolume charge (and the radius) in the area within the volume charge density. Note the permittivity of the material! E=