An analytical method for exactly drawing current and equipotential lines in a conditional rectangular compound region consisting two anisotropic media is presented. In the region, the internal boundary of two media is on the diagonal line of the rectangle and the electrodes are attached to opposite sides.
In the method of this paper, first, the rectangular region is transformed to a mirror anti symmetrical region with a different resistivity tensor from that in the original region, under some limitations. By the transformation, however, the field continuity on the boundary is conserved. In the transformed region, the angles of incidence and refraction for the current and equipotential lines on the boundary can be determined, respectively. Next, another compound region with the known electric field and with the same boundary conditions as those in the transformed region is considered. Thus, the current and equipotential lines in the rectangular region can be easily obtained by mapping those in the region finally considered because each region in the analytical procedure gives us the same solution for the electric current field to be solved.
View full abstract