Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

Table 1

Relationship between the 𝑤 and 𝑧 planes for the capacitor of semicylindrical plates.

𝑤 plane	𝑧 plane
𝑤1=𝑅0	𝑧1=0
𝑤2=𝑅0𝑒^𝑖⋅𝛼	𝑧2=1
𝑤3=−𝑅0𝑒^−𝑖⋅𝛼	𝑧3=−𝛽^2
𝑤4=−𝑅0	𝑧4=∞
𝑤5=−𝑅0𝑒^𝑖⋅𝛼	𝑧5=𝛽^2
𝑤6=𝑅0𝑒^−𝑖⋅𝛼	𝑧6=−1