I need to have question 3.4.2 answered, but it references the other two, so I included them as well. Thank you.
3.2.4. A ring of charge of radius a has a linear charge density of ⍴l C/m that is uniformly distributed around the ring. Determine the electric field at a distance d along a line perpendicular to the ring and centered on it. Evaluate this result for a distance much greater than the radius of the ring. This result at a large distance away should be reduced to that for a point charge. Why?
3.2.5. Determine the electric field of a disk of charge of radius a having a uniform charge distribution of ⍴ C/m^3 over its surface at a distance d away from its center and on a line through its axis. You will need the integral ∫r/(d^2 - r^2)^(3/2)dr = -1/√(d^2 - r^2). Evaluate this area, at a distance much larger than the radius of the disk. This result at a large distance should be reduced to that for a point charge. Why? [E = ⍴s/2ɛ0[1 - d/√(d^2 - a^2)] az, E = 𝜋a^2 ⍴s/4𝜋ɛ0d^2 az d»a. At large distances away, the disk of charge can be thought of as a point charge equal to the total charge contained in the disk: Q = 𝜋a⍴s
3.4.2. For the problem of a ring of charge in Problem 3.2.4 and the disk of charge in Problem 3.2.5, can Gauss' law be used to determine the electric field at a distance from the center and on a line perpendicular to the ring or disk? If not, why not?