6.1

For an AC magnetic field tangential to a conducting half-space, show that the real and imaginary parts of the eddy current density are proportional to and . Show that Re( J _x) changes sign (is zero) at characteristic depths z = (4 n + 3) ??/4 inside the metal while Im( J _x) changes sign at z = (4 n + 1) ??/4, where n = 0,1,2

6.2

Model a current loop of radius r ₀ as a single node in axial symmetric geometry a height ? above a semi-infinite, permeable conducting half-space in Figure E-6.2. Plot the imaginary z-component magnetic field at the center of the current loop as a function of frequency using Label Mover.

6.3

Model a current loop of radius r ₀ as a single node in axisymmetric geometry a height ? above a plate of thickness d, conductivity ?, and permeability ? ₀. Compare the eddy current density along a radial contour on each surface and at the center of the plate to the analytical expression J _eddy = - i ??A _?, where

where and the upper and lower surfaces of the plate are located at z = 0 and z = -d, respectively.

6.4

Show that for a current loop of radius r ₀ above a perfectly conducting semi-infinite half-space the vector potential has the form

where z