A very long cylinder of radius 2b with a co-axial cylindrical hole of radius b. (Co-axial means the two cylinders have the same axis.) The charge per volume p is constant in the solid shell b 2b)? lenc = denc = E =

2. Consider an insulating spherical shell of inner radius a and outer radius b. a. If the shell has a net charge Q uniformly distributed over its volume, find the vector electric field in all regions of space (r b) as a function of r. b. Now assume that the shell has a non-uniform charge density given by r2 p(r) = Po ab What is the net charge of the shell? c. For the charge distribution in part (b), find the vector electric field in all regions of space (r b) as a function of r.

A uniformly charged conducting sphere of 1.2m diameter has a surface charge density of 1.8µC/m?. Find the net charge on the sphere. b. What is the total electric flux leaving the sphere? What is the magnitude of the electric field at point P, 0.7m from the center of the sphere?

The Electric Field of a Charged Cylinder and a Concentric Cylindrical Shell. A non-conducting cylinder of radius a is charged with charge density p(r) = p.r, where r is the distance from the cylinder axis. The cylinder is placed inside a shell with cylindrical inner and outer radii b and c, respectively. The outer shell is charged with a uniform charge density p(r) = Po. The cylinder and the shell are concentric (see figure). D B b 0 Derive the formulas for the magnitude of the electric field at points A, B, C, and D. Guidance: 1. If required by the formulas, specify Coulomb's force constant through the Vacuum Permittivity, E = 1/4nk instead of Coulomb's onstant, k. 2. Type epso, rhoo, and pi, if the respective symbols Eo,Po, and n, are required.