Coaxial perfectly conducting circular cylindrical electrodes make contact with a uniformly…

Coaxial perfectly conducting circular cylindrical electrodes make contact with a uniformly conducting material of conductivity σ in the annulus 596bd61b b30f 4be5 b6ca 0631b3d1ec21, as shown in Fig. P11.3.2. The length b46af941 25c6 476b 8c28 8dfc9cb331ba is large compared to a. A voltage source v drives the system at the left, while the electrodes are “open” at the right. Assume that 6b040657 bd2e 486a ae04 edfb54f04012 is so slowly varying that the voltage can be regarded as independent of 4eda1957 4486 4b69 9a48 2151bf5eedd5.

Fig. P11.3.2

33971eed ba94 405f ac91 5d0e00031f68

(a) Determine 837a4656 0359 42b9 a285 11eb76547bef, and 1e0a494c 84d3 4214 b51c 69cb584453d3 in the annulus.

(b) Evaluate the Poynting power flux density 008fed17 c200 41e0 9896 9d3642cb4067 [as given by (3)] in the annulus.

(c) Use S to evaluate the total power dissipation by integration over the surface enclosing the annulus.

(d) Show that the same result is obtained by integrating dcfe266a 991c 4e12 9948 fbc7812ab4f8 over the volume.

(e) Evaluate S as given by (23), and use that distribution of the power flux density to determine the total power dissipation.

(f) Make sketches of the alternative distributions of S.

(g) Show that the input power is vi, where i is the total current from the voltage source.

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