Question

The cylindrical surface p= a is a thin dielectric sheet carrying a harmonic surface current density K(a, \phi, z, t)=\hat{\phi} K_{0} \exp (j a t) \quad(A / m) Assume the medium is free space and the cylinder is of infinite length and the electric and magnetic fields outside the cylinder (p> a) are zero. (a) Write the partial vector differential equation for the phasor vector magnetic potential Ã. (b) What component of the phasor vector magnetic potential will be non-zero,explain? On what cylindrical coordinate does this component depend,explain? (c) Write the ordinary differential equation satisfied by this component. (d) Find its solution valid for p < a. The solution will contain an undetermined constant Ao. (e) Determine the phasor vector electric field Ẽ and phasor vector magnetic field H in terms of Ao. (f) Use Ampere's law to relate Ao with Ko.

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