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 
, as shown in Fig. P11.3.2. The length 
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 
is so slowly varying that the voltage can be regarded as independent of 
.
Fig. P11.3.2
(a) Determine 
, and 
in the annulus.
(b) Evaluate the Poynting power flux density 
[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 
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.
