Please see attached file 4. for the following problems:
6. At each point on the surface of the cube shown in Figure 23-27, the electric field is parallel to z-axis. The length of each edge of the cube is 3.0 m. On the top face of the cube, E = -34k N/C, and at the bottom face E = +20k N/C. Determine the net charge contained within the cube.
29. A long, straight wire has fixed negative charge with a linear charge density of magnitude of 3.6 nC/m. The wire is to be enclosed by a coaxial, thin walled nonconducting cylindrical shell of radius 1.5 cm. The shell is to have positive charge on its outside surface with a surface charge density sigma that makes the net external electric field zero. Calculate sigma.
9. A nonconducting sphere has radius R = 2.31 cm and uniformly distributed charge q = + 3.50 fC. Take the electric potential at the sphere's center to be V0 = 0. What is V at radial distance (a) r = 1.45 cm, and (b) r = R.
54. A hollow metal sphere has a potential of +400 V with respect to ground (defined to be at V = 0) and a charge of 5.0 * 10^(-9) C. Find the electric potential at the center of the sphere.
The solution is comprised of detailed calculations of the electric field and electric potential when the charges are uniformly distributed over cube, long straight wire, and sphere, etc.