Field and Wave Electromagnetics 2nd Edition by David Cheng

تمرين 26

A ground connection is made by burying a hemispherical conductor of radius 25 (mm) in the earth with its base up, as shown in Fig. Assuming the earth conductivity to be 10 -6 S/m, find the resistance of the conductor to far-away points in the ground. ( Hint: Use the image method in Problem.)
Figure: Hemispherical conductor in ground

Problem:
Justify the statement that the steady-current problem associated with a conductor buried in a poorly conducting medium near a plane boundary with air, as shown in Fig. 1 can be replaced by that of the conductor and its image, both immersed in the poorly conducting medium as shown in Fig. 2.
Figure: Steady-current problem with a plane boundary
Figure 1: Conductor in a poorly conducting medium near a plane boundary.

Figure 2: Image conductor in conducting medium replacing the plane boundary.