The fossil-fuel era is coming to an end. Thus far, it has spanned about 250 years from 1760 to 2011, and according to the historical record, these years have represented a period of immense change in technological terms, encompassing brilliant scientific breakthroughs and engineering innovation. But, what history generally fails to report is that it has also been a period of inexcusable profligacy in relation to our treatment of the planet's initially bountiful energy supplies. S.E. Lindsay's desire, in 1920, for the responsible delivery of engineering progress has not occurred. This is largely due to the fact that, despite their finiteness, the primary sources of power: coal, oil and gas, have been inordinately cheap throughout this time span, since these products of ancient sunlight, and the pollution they cause when combusted, have largely been treated as uncosted 'externalities' in the classical economic science, which underpins our global capitalist system.

A brief history of electrical science. To levitate in a vacuum an object, which is heavier than air in defiance of the force of gravity here on the surface of Earth, scientists and engineers mainly enlist forces familiar to practitioners of electrical science. These forces are represented by the electrostatic field, the magnetostatic field and electromagnetic fields (including optical manifestations). Examples of 'levitation', using acoustic pressure, have also been reported, but this is pseudo-levitation, like aerodynamic lift, since it cannot be procured without the presence of a gas. Any other forms of 'levitation' are purely in the deceived or deluded minds of the beholders. In this chapter, we will engage only with the electrical forces, whose provenance and fundamental nature will be elucidated below.

The evolution of frictionless bearings in instruments and machines, including the contactless manipulation of objects, has been advanced predominantly by adopting electromagnetic methods, rather than electrostatic methods, to create levitation and suspension systems as described in Chapter 4. This is partly because, even more so than conventional magnetic levitation, which is only conditionally stable as we have already discovered, electrostatic suspension has generally been considered to be a particularly fraught area of technology because the Earnshaw's rules influence stability more acutely. Nevertheless, electrostatic suspension offers some significant advantages over magnetic techniques.

Within the boundaries imposed by our exploration of the technology of levitation and suspension, this chapter addresses diamagnetic phenomena in three categories. These are: 1. Non-metallic materials: In this case, diamagnetism is generally a very weak property that is usually swamped by paramagnetic effects. Biological materials are diamagnetic, very graphically demonstrated by a now famous experiment in which a frog is floated in a powerful magnetic field. The physiological repercussions for the frog are not recorded. 2. Metals: In a non-magnetic environment, 'good' conductors are either weakly diamagnetic or weakly paramagnetic. However, in a changing magnetic field, currents are induced in a conductor. In accordance with Lenz's law, these currents adopt circulation directions that generate secondary fields opposing the original field. In effect, the conductor behaves in a strongly diamagnetic manner. This effect is used widely in levitation systems from bearings to trains. 3. Superconductors: These represent the optimum in diamagnetism by exhibiting a magnetic susceptibility of -1. The strength of the levitation forces available with type I superconductors has provided a new impetus to developments in levitation, although it comes with the disadvantage of the need to provide supercooling. High temperature, type II superconducting materials, within which strong magnetic fields can be trapped, have become a source of very powerful permanent magnets at liquid nitrogen temperatures. This relatively recent development has also given a considerable boost to the search for successful, cost effective levitation systems.

By employing basic field relations for the dominant TM₁₁ mode of a waveguide ring resonator together with fundamental energy expressions for cavity resonators, the primary requirements that must be met by a resonant cavity-based magnetic field levitation system are established. When these requirements are fulfilled stable levitation of a 'free' conducting wall, or 'float' of a waveguide-based ring-resonator supporting a TM resonance is predicted. In particular, it is shown that the available levitating force (Lorentz force) is substantially larger than the gravitational force for TM_11n cavity resonators where n is small-ideally zero. For systems designed to operate at mm-wave frequencies (100 GHz), strong levitation is available even with modest drive powers in the milliwatt range. In fact, experimentation on a TM₁₁₁ mode waveguide ring, resonating in the microwave, rather than the mm-wave range of frequencies, has suggested that a 1 mm thick floating wall weighing 15.88 mg, can be levitated with drive power levels in the 5-15 W range. The TM₁₁₁ mode used in these experiments is reported to have displayed a Q level in excess of 20,000 with the floating wall in its levitated position.

While Maxwell's equations are applicable to virtually all macroscopic electrical phenomena, they are often mathematically too difficult to apply directly to realistic structures. Circuit board elements, such as apparently simple capacitors and inductors, come into this category. However, for such elements, provided they can be considered to be very small relative to the wavelength in free-space at the operating frequency of the electrical system, an analysis technique termed lumped element circuit theory furnishes powerful insight into the behaviour of quite complex multi-component networks.