The Lorentz force that a magnetic field exerts on a moving charge carrier is perpendicular to the direction of motion and to the magnetic field. Since both electric and thermal currents are carried by mobile electrons and ions, a wide range of galvanomagnetic and thermomagnetic effects result. The effects that occur in an isotropic polycrystalline metal are illustrated in Fig. 20.1. As to be expected, many more cross-coupled effects occur in less symmetric solids. The galvanomagnetic experiments involve electric field, electric current, and magnetic field as variables. The Hall Effect, transverse magnetoresistance, and longitudinal magnetoresistance all describe the effects of magnetic fields on electrical resistance. Analogous experiments on thermal conductivity are referred to as thermomagnetic effects. In this case the variables are heat flow, temperature gradient, and magnetic field. The Righi–Leduc Effect is the thermal Hall Effect in which magnetic fields deflect heat flow rather than electric current. The transverse thermal magnetoresistance (the Maggi–Righi–Leduc Effect) and the longitudinal thermal magnetoresistance are analogous to the two galvanomagnetic magnetoresistance effects. Additional interaction phenomena related to the thermoelectric and piezoresistance effects will be discussed in the next two chapters. In tensor form Ohm’s Law is . . .Ei = ρijJj , . . . where Ei is electrical field, Jj electric current density, and ρij the electrical resistivity in Ωm. In describing the effect of magnetic field on electrical resistance, we expand the resistivity in a power series in magnetic flux density B. B is used rather than the magnetic field H because the Lorentz force acting on the charge carriers depends on B not H.
Rotation induced by uniform and non-uniform magnetic fields in a conducting fluid carrying an electric current
