# 5. Consider a very long coaxial cable, comprised of concentric cylindrical conductors with some insulating gap…

5. Consider a very long coaxial cable, comprised of concentric cylindrical conductors with some insulating gap between them. In particular, the inner solid cylindrical conductor has a radius, a, and carries a total, axial current, I. However, this current is not distributed uniformly along its circular cross section. In particular, the current density of this inner conductor is J(r) = Jovi where Jo is a positive constant that is to be determined and r labels the radial distance away from the cylindrical wire’s axis of symmetry. Furthermore, the outer conductor is hollow, has a negligible thickness, and has a radius, b> a. This conductor carries a total, axial current, 31, but in the opposite direction to the inner conductor’s current. Answer the following parts while showing all of your work and reasoning. (40 (a) Draw a picture of the coaxial cable described above, with relevant information indicated on the drawing, (b) Determine Jo in terms of the other given quantities. (e) Determine the magnetic field of this coaxial cable everywhere. (a) Plot the magnetic field of this coaxial cable as a function of the radial distance away from the common axis of symmetry, (e) Coaxial cables are known for their shielding capabilities. What does “shielding” mean in this context, and how can this cable be modified to shield better? Explain.