Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

The notion of $d{{0}{0ex}}e{{0}{0ex}}m{{0}{0ex}}a{{0}{0ex}}g{{0}{0ex}}n{{0}{0ex}}e{{0}{0ex}}t{{0}{0ex}}i{{0}{0ex}}z{{0}{0ex}}a{{0}{0ex}}t{{0}{0ex}}i{{0}{0ex}}o{{0}{0ex}}n$ is encountered in many areas of science and engineering that involve interactions between fields and finite-sized objects. In magnetism, demagnetizing effects account for the distortion of the magnetic fields around a specimen, and connect induced magnetic moment to the applied magnetic field. The authors derive analytic expressions for the total magnetic moment, and then use numerical finite-element solutions of Maxwell's equations to find the effective demagnetizing factors for various nonellipsoidal geometries commonly encountered in experiments. This work provides practical guidelines for data analysis for superconducting and magnetic samples.