Classical Electrodynamics · Problem 12.20

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · superconductor-surface-impedance

Problem

A uniform superconductor with London penetration depth λL\lambda_L fills the half-space x>0x > 0. The vector potential is tangential and for x<0x < 0 is given by Ay=(aeikx+be−ikx)e−iωtA_y = (ae^{ikx} + be^{-ikx})e^{-i\omega t} Find the vector potential inside the superconductor. Determine expressions for the electric and magnetic fields at the surface. Evaluate the surface impedance ZsZ_s (in Gaussian units, 4π/c4\pi/c times the ratio of tangential electric field to tangential magnetic field). Show that in the appropriate limit your result for ZsZ_s reduces to that given in Section 12.9.

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