Coaxial perfectly conducting circular cylinders having outer and inner radii a and b,…

Coaxial perfectly conducting circular cylinders having outer and inner radii a and b, respectively, form the transmission line shown in Fig. P13.1.4.

(a) If the conductors were “open circuit” at ef5a56a7 7660 446a b0b7 7a9bb2b03e9band driven by a voltage source 1da20476 9c62 4d25 881e 21ecce939079 at 45fa083b da4f 454a a39f b3c57bf17357, show that the EQS electric field is radial and given by 2fd172d5 94e1 47a9 9bc0 f396873ca28f.

(b) If the conductors were “shorted” at 49b77672 fd3d 4de5 aaaf 5a972ae2f00e and driven by a current source 5c11a953 27d6 47ea a350 24adfb763e49 at 45fa083b da4f 454a a39f b3c57bf17357, show that the MQS magnetic field intensity is φ directed and given by a7f483f0 3513 4884 8aa6 390dd800a50c. (c) With the motivation provided by these limiting solutions, show that solutions to all of Maxwell’s equations (in the region between the conductors) that satisfy the boundary conditions on the surfaces of the coaxial conductors are

a6cc2b92 8e65 45c1 a529 43c8965adbe9

provided that 1da20476 9c62 4d25 881e 21ecce939079 and 5c11a953 27d6 47ea a350 24adfb763e49 are now functions not only of 5a37d1f6 2bfc 48d8 bd60 351d6cd13bc3 but of 37709a59 0843 4688 b17c 9c8b19e14742 as well that satisfy equations taking the same form as (13.1.2) and (13.1.3).

bebf80e3 cf04 4aa1 ab2d 7dfa61f65fc3

Fig. P13.1.4

159a18b6 898d 4748 b463 19b6eaabc848

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