HOW A SUPERCONDUCTOR SUPPORTS A MAGNET, HOW MAGNETICALLY SOFT IRON ATTRACTS A MAGNET, AND EDDY CURRENTS FOR THE UNINITIATED

It is shown how an infinite superconducting slab supports a permanent ("hard") magnet against gravity. The equilibrium position is found, using the method of images and the property that superconductors expel magnetic flux, and then the supercurrents (in the approximation that they are localized at the surface) are explicitly determined, using the boundary condition associated with Ampere's law. This calculation, which does not require the London equation (although a brief discussion of its effects is given), can be done by motivated freshmen. (Measurements by Heller on high-Tc samples yield a flotation height about half the predicted value; this is attributed to incomplete screening of the applied field, due to penetration by magnetic flux lines.) From this example two subjects can then be discussed that normally precede a discussion of superconductivity. First, these supercurrents are equal and opposite to the Amperian surface currents that attract a permanent magnet to an infinitely permeable ("soft") magnetic slab (the image method yields equal and opposite images if the superconductor supporting the permanent magnet is replaced by an infinitely permeable material). Moreover, these supercurrents are the same as the initial eddy currents generated if a solenoid is suddenly energized or if a permanent magnet suddenly materializes above a conducting slab. Following a discussion of Maxwell's theory of eddy currents in thin conducting sheets, the time-development of this initial eddy current distribution is obtained.