In the system shown in cross-section in Fig. P10.4.5, a thin sheet of conductor, having thickness…
In the system shown in cross-section in Fig. P10.4.5, a thin sheet of conductor, having thickness ∆ and conductivity σ, is wrapped around a circular cylinder having infinite permeability and radius b. On the other side of an air gap at the radius 
is a winding, used to impose the surface current density 
sin 2φ
, backed by an infinitely permeable material in the region 
.
(a) The current density varies so rapidly that the sheet behaves as an infinite conductor. In this limit, show that Ψ in the air gap is
(b) Now suppose that the driving current is so slowly varying that the current induced in the conducting sheet is negligible. Show that
Show that the early and long-time responses do indeed match the results found in parts (a) and (b).
Fig. P10.4.5
