A long, straight wire is aligned with the z-axis. It has constant linear charge density λ and is surrounded by a coaxial cylindrical shell of radius R and surface charge density σ = −λ/(2πR). The region 0 < s < R/2 is filled with a linear dielectric of electric susceptibility χe, and there is no dielectric anywhere else. Label regions of space as follows (s is the distance from the z axis): region A (0 < s < R/2), region B (R/2 < s < R), and region C (s > R).
(a) Find E, P, and D in all three regions.
(b) For each of the above three fields, explain whether there a discontinuity when moving radially
outward from s = (R/2)− to s = (R/2)+. What is the origin of the discontinuity if one exists?
(c) For each of the above three fields, explain whether there a discontinuity when moving radially
outward from s = R− to s = R+. What is the origin of the discontinuity if one exists?
A long, straight wire is aligned with the z-axis. It has constant linear charge density λ...
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