Atomic magnetic dipole moments are spin origin

operate at low voltage levels; (2) magnets for high-energy particle accelerators; (3) higher-speed switching and signal transmission for computers; and (4) high-speed magnetically levitated trains, wherein the levitation results from magnetic field repulsion. The chief deterrent to the widespread application of these supercon-ducting materials is, of course, the difficulty in attaining and maintaining extremely low temperatures. Hopefully, this problem will be overcome with the development of the new generation of superconductors with reasonably high critical temperatures.

S U M M A R Y

With rising temperature, increased thermal vibrations tend to counteract the dipole coupling forces in ferromagnetic and ferrimagnetic materials. Consequently, the saturation magnetization gradually diminishes with temperature, up to the Curie temperature, at which point it drops to near zero; above Tc, these materials are paramagnetic.

Below its Curie temperature, a ferromagnetic or ferrimagnetic material is com-posed of domains—small-volume regions wherein all net dipole moments are mutu-ally aligned and the magnetization is saturated. The total magnetization of the solid is just the appropriately weighted vector sum of the magnetizations of all these domains. As an external magnetic field is applied, domains having magnetization vectors oriented in the direction of the field grow at the expense of domains that have unfavorable magnetization orientations. At total saturation, the entire solid is a single domain and the magnetization is aligned with the field direction. The change in domain structure with increase or reversal of a magnetic field is accom-plished by the motion of domain walls. Both hysteresis (the lag of the B field behind the applied H field) as well as permanent magnetization (or remanence) result from the resistance to movement of these domain walls.

Information storage is accomplished using magnetic materials in both needle-shaped particulate and thin-film forms.

Superconductivity has been observed in a number of materials, in which, upon cooling and in the vicinity of absolute zero temperature, the electrical resistivity vanishes. The superconducting state ceases to exist if temperature, magnetic field, or current density exceeds the critical value. For type I superconductors, magnetic field exclusion is complete below a critical field, and field penetration is complete once HC is exceeded. This penetration is gradual with increasing magnetic field for type II materials. New complex oxide ceramics are being developed with relatively high critical temperatures, which allow inexpensive liquid nitrogen to be used as a coolant.

R E F E R E N C E S

Q U E S T I O N S A N D P R O B L E M S

Scientific American, Vol. 217, No. 3, September 1967, pp. 222–234.

(a) What is the magnitude of the magnetic field strength H?

(b) Compute the flux density B if the coil is in a vacuum.