Answer Happy

b) Consider a long cable of two coaxial conducting cylindrical shells with radii a and 2a, which carry charges + per unit length. The interior between the shells is filled with a material with relative permeability , >1 and relative permittivity €, = 1. (i) Determine the E-field everywhere. Comment on any symmetry assumptions you make. [4] [5] (ii) Now determine the magnitude of the potential difference between the two shells, and hence deduce an expression for the capacitance of the cable per unit length. (iii) Now consider a current I flowing down the inner shell and back up the outer shell. Compute the B-field between the shells. Comment on any symmetry assumptions you make. [4] μομεΙ Verify that A = 2π In pe, is the correct vector potential between the shells. You may use the expression for the curl operator in cylindrical coordi- nates, 1 (0(pK) ƏK,` V x K = - (²3/0 ako əz €p+ - (³K₂ - Ək₂ əz ap e + (³oh ak) др (iv) Compute the macroscopic Poynting vector and comment on its direction. (v) Determine the magnetic flux 3 through the current loop formed by the cable, and deduce an expression for the self-inductance per unit length. e.. [2] [2] [4]