1. A spherical shell with inner and outer radii, a and b respectively, carries a uniform charge with charge density rho_v. a. find the total charge in the shell. b. Use Gauss's Law to find the electric field intensity everywhere in space. c. If a point charge Q is placed at the center of the shell, find the force experienced by the charge Q. 2. Four equal charges are located at the corners of a square of radius a. Assume that the square is in the xy-plane, centered at the origin and its sides are parallel to the x and y axes, a. find the electric field intensity along the z-axis. b. find the electric potential at any point on the z-axis. c. find the energy in the system of charges. 3. Assume the electric flux density is given by D=2cos(theta)/r^3a_r+sin(theta)/r^3a_theta C/m^2 a. Find the charge density rho_v b. Find the electric potential V. c. Find the energy stored in spherical region r>3m

1. A spherical shell with inner and outer radii, a and b respectively, carries a uniform charge with charge density rho_v. a. find the total charge in the shell. b. Use Gauss's Law to find the electric field intensity everywhere in space. c. If a point charge Q is placed at the center of the shell, find the force experienced by the charge Q. 2. Four equal charges are located at the corners of a square of radius a. Assume that the square is in the xy-plane, centered at the origin and its sides are parallel to the x and y axes, a. find the electric field intensity along the z-axis. b. find the electric potential at any point on the z-axis. c. find the energy in the system of charges. 3. Assume the electric flux density is given by D=2cos(theta)/r^3a_r+sin(theta)/r^3a_theta C/m^2 a. Find the charge density rho_v b. Find the electric potential V. c. Find the energy stored in spherical region r>3m