Hall effect Classical

Information about the sign of the mobile charge may be obtained from another observable, the Hall coefficient. The Hall effect is observed when a current carrying conductor (current in direction x, say) is placed in a magnetic field H perpendicular to the current direction, the z direction say. An electric field is formed in the direction y perpendicular to both the current and to the applied magnetic field, and the ratio A u = Sy/jfHz is the Hall coefficient. A theory done on the same classical level as used above leads to... 

As indicated in an earlier review," the Hall effect has been the subject of numerous investigations. The Hall constant Rjj is defined by the classical electric field equation... 

The Hall effect measurements also show that the mobility increases as the temperature is lowered, a trend predicted by the quantum relations (9.76) or (9.80) but completely opposite to the classical behaviour (9.62). This trend had also been noted previously in low-temperature high-field studies by Engelhardt Riehl (1966), where also there was evidence of proton trapping. 

Figure 8.2. Diagrams a) sectional view (from [BAR 11]) and b) three-dimensional representation, of a classic Hall-effect thruster. The holes in the anode are generally very small indeed (around 100pm in diameter), and the electrical field is strongest around the outlet vent...

Part Two of this volume is entitled Introduction. It too has four chapters. Chapter 5 presents a study of the influence of diverse fields on flames Chapter 6 discusses a classic application of the Peltier effect Chapter 7 is devoted to metal/plasma interaction, and more speciffcally to the Langmuir probe, and finally Chapter 8 discusses space propulsion by the Hall effect. 

The expression derived in Eq. (7.38) is defined as the Hall conductivity an it is the ratio of the current in the x direction to the effective electric field Ey in the perpendicular direction, as usually defined in the classical Hall effect in electrodynamics. In more general terms, this ratio can be viewed as one of the off-diagonal components of the conductivity tensor cr, (f, j = x, y), which relates the current to the electric field ... 

The Hall effect indicates p-type behavior as well, and based on classical theory an interband thermal activation of the carriers of 1.52 eV was derived from the slope. This agrees quite well with the gap energy (101). 

The Hall effect of boron carbide is small (Fig. 35a and b). It depends on composition and temperature (14,147-149). Because the calculation of the Hall mobility from the measured Hall constant depends strongly on the electronic transport mechanism, which for boron carbide has not yet been finally solved, the mobilities calculated after classical theories and shown in Fig. 35 are somewhat questionable. Hall effect and magnetoresistance were measured up to 15 T (Figs. 36 and 37) (157). The behavior expected from classical theory was confirmed in a large range, and for B > 13 T the magnetoresistance seems to indicate beginning Shubnikov-de Haas oscillations. The transport parameters obtained are listed in Table 3. 

Although Fe304 is cited as the classical example of this effect, it should be noted that the transition temperature is about four times smaller than is predicted from electrostatic considerations. Also the room-temperature Hall mobilities of the charge carriers are 0.5 cm2/V-sec (719), which might be thought to represent narrow-band conductivity. (In Fe304 there arc 3.5 t2g electrons per B-site cation, so that if R < Rc, and upper H-site t2g band, which is split from a lower t2g band by intraatomic exchange via the localized eg electrons, would be one-sixth filled.) However, intermediate mobil-... 

The ideas about the relationship between work and health have changed dramatically since the 1980s. In the classic view, the employee, in particular his or her "weak" personality, was held accountable for stress problems such as psychosomatic complaints, sleeping problems, and an unhealthy lifestyle. It has now been demonstrated (see Karasek Theorell, 1990, for a review) that some fectors in the work environment have negative effects on health and well-being. In a longitudinal study in which more than 7,000 Swedish employees were monitored during a 9-year period, it was found that the risk of cardiovascular diseases increased and life expectancy was estimated to be shortened by 7 years due to unhealthy psychosocial factors in the work environment (Johnson, Hall, Theorell, 1989). 

An alternative analysis of colloidal interaction and stability based on classical solution thermodynamics has been proposed independently by Hall (1972) and Ash etal. (1973) and the practical implications with particular interest in the effects of polymers and surfactants has been discussed by Pethica (1986). In this theory, the forces between particles are governed in a straightforward way by the adsorptions of the components of the system and their dependence of particle separation and chemical potentials (which are defined by the composition) according to the equation... 

---