Damping forces on an oscillating magnet near a fixed conducting disc

Developed an analytical model of electromagnetic damping for a magnetic dipole undergoing small axial oscillations near a coaxial conducting disk of finite radius and thickness. I derived the damping coefficient independently using an energy-dissipation approach and a direct-force approach, and investigated their discrepancy when the magnetic field varies appreciably across the finite disk. I then developed a radial power-series expansion of the magnetic field using Laplace’s equation, obtaining recursion relations for the expansion coefficients and a general expression retaining both finite-radius and finite-thickness effects. I further derived an asymptotic expansion in the dimensionless parameters R/Z and h/Z, including their coupled corrections.