Mutual inductance of coils on a cylinder of infinite length

Magnetic coupling between two thin circular loops coaxial with a cylinder of infinite length and permeability μ is considered. Numerical values of the mutual inductance as a function of relative permeability and the distance between the two loops are presented for the static case. These values represent an upper bound for the low-frequency mutual inductance between two thin circular loops coaxial with a cylinder of finite length located in a conducting half-space. Such a model can be used in the study of a magnetic down-hole-to-surface communication link for oil and gas well testing.