Convective magnetic fields in a dispersive half-space

• Published in: Proceedings of the Royal Society. A, Mathematical and physical sciences Mathematical and physical sciences, 2010-08, Vol.466 (2120), p.2383-2400
• Main Author: Barton, Gabriel
• Format: Article
• Language: English
• Subjects: Approximation; Charge; Conductors (devices); Coordinate systems; Dielectric materials; Dispersions; Electric current; Fields In Dispersive Media; Half spaces; Insulators; Magnetic fields; Magnetic Shielding; Mathematical analysis; Mathematical models; Parallel lines; Physics; Plasmons; Stagnation point; Trajectories; Velocity-Field Penetration
• ISSN: 1364-5021; 0962-8444; 1471-2946
• DOI: 10.1098/rspa.2009.0551

It is known that inside a material half-space the magnetic field B owing to the currents generated there by a slowly moving exterior charge (velocity u) is almost the same whether the material is a good Ohmic conductor or a highly refractive non-dispersive/non-dissipative insulator. By contrast, the drag force experienced by the charge is completely different for conductors and insulators. To gain insight into the somewhat surprising coincidence regarding B fields, we study a microscopic model whose macroscopic Drude-type dielectric function ε(ω) can fit a fair variety of dispersion and dissipation. We look for B only to first order in u/c, but with otherwise arbitrary u. Then, B is given by the Biot—Savart rule. The term linear in u follows directly from the polarization produced as if electrostatically by the charge in its instantaneous position, and depends only on ε(0), the strictly static (zero frequency) response function; only the corrections of higher order in u depend on just how ε varies with ω, and we determine the first such corrections.