Magnetic and magnetic gradient fields due to a finite line segment

Abstract

We derive the closed-form expressions for the magnetic field and magnetic gradient tensor produced by a finite line segment with uniform magnetization. Following the classical approach, we firstly derive the gravitational potential for a line segment by a line integral and derive the gravity vector and gravity gradient tensor through differentiations with respect to Cartesian axis. The magnetic field expression is then obtained from the gravity gradient tensor using Poisson's relation. We verify the validity of the solutions numerically through comparison with the result from a different formulation as well as with a dipolar field. The results provide an efficient means to calculate the ground and drone-measured magnetic responses in environmental and engineering applications such as locating abandoned ferromagnetic pipe lines and characterizing well casings and flow lines in the legacy oil and gas fields.