5. A cylinder with infinite length, relative permittivity of &,, and radius of R is charged with uniform volume charge density of p. Using Gauss' law, derive the electric field, E, and electric flux density, D, inside and outside of the cylinder. Plot the electric field versus distance and discuss boundary conditions. (Points: 15%) 6. A positive point charge Q is at the center of a spherical conducting shell of an inner radius R; and an outer radius Ro. Determine and plot the electric field E as functions of the radial distance R. Note that as the spherical shell is conducting (metal), the electric field in its inside should be zero. Ri (Point: 15%) I+ Conducting shell 7. A sphere is charged with nonuniform charge density of p(r) = Po where po is a constant and "a" is the sphere radius. The material relative permittivity is &. Using Gauss' law, derive the electric field inside and outside of the sphere. (Point: 15%) 8. Summarize the most important concepts and theories you have learned in this chapter in a maximum of one page. (Points: 15%)

Fig: 1