12. Two long concentric and hollow conducting cylinders of radii a and b (a

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12 Two Long Concentric And Hollow Conducting Cylinders Of Radii A And B A B Carry Equal And Opposite Current I Each 1 (70.17 KiB) Viewed 34 times

12. Two long concentric and hollow conducting cylinders of radii a and b (a<b) carry equal and opposite current I. Each cylinder has a negligible thickness L<<a. The space between the two conductors is filled with a diamagnetic material of relative permeability (Fig. 5). 14 Figure 5 14, (a) Show that, in the approximation of L<<a,b, the areas traversed by the inner and outer currents are given, respectively, by A₁ = 2ral and A₂ = 2rbL. Calculate the corresponding current densities. [3] (b) Draw the direction of the magnetic field generated by the inner current. [1] (c) Calculate the amplitude of the B, H, and M fields for distances r <a. [2] (d) Calculate the amplitude of the B, H, and M fields between the two conductors (b>r> a). [5] (e) Calculate the amplitude of the B, H, and M fields outside of the whole system (r>b). [2] (f) Discuss how the fields between the two conductors will change if the diamagnetic material is removed. [2] (g) Discuss if wrapping the whole system in a paramagnetic material would change the magnetic field distribution generated by the system [2] (h) In what direction should an external observer with the right velocity move in order not to observe any magnetic field between the two conductors? What type of field would the observer see for r> b? [3] va