Magnetization vector definition

We return to the definition of the Lagrangian function, Eq. (3.36.2) for a particle with mass m and electrical charge e subjected to a magnetic vector potential A and to a scalar potential 4> ... 

By definition, a magnetic moment of substance per unit volume is magnetization M = xH. For an anisotropic material, the magnetization vector components are Ma = and the contribution to the fi-ee energy density of the mesophase from the magnetic field is given by [1] ... 

Any set of constitutive relationships such as (10) and (11) or (13) and (14) is a reflection on the macroscopic scale of the microscopic behavior of the individual molecules which comprise the substance. The connection between the macroscopic and the microscopic is provided through the statistical interpretation one can give to the polarization vector P and the magnetization vector M which relate D with E and B with H through the auxiliary definitions... 

Fig. 4.16 Definition of the polar angles 9, c(). k is the wave vector of the emitted y-ray. The z-axis may be defined by the direction of a magnetic field...

To illustrate the use of the vector operators described in the previous section, consider the equations of Maxwell. In a vacuum they provide the basic description of an electromagnetic field in terms of the vector quantifies the electric field and 9C the magnetic field The definition of the field in a dielectric medium requires the introduction of two additional quantities, the electric displacement SH and the magnetic induction. The macroscopic electromagnetic properties of the medium are then determined by Maxwell s equations, viz. 

In the usual texts a multipole expansion involving spherical Bessel functions and spherical vector harmonics is also introduced [16,23,23,26]. The fields from electric and magnetic dipoles correspond to the lowest-order terms ( =1) in the expansion. If we define dipole by this expansion then our toroidal antenna is an electric dipole. In any event, the fields away from the source are the same. This is perhaps a matter of consistency in definitions. 

The unit vector components of the classical magnetic fields Ba>, Ba and B<3> in vacuo are all axial vectors by definition, and it follows that their unit vector components must also be axial in nature. In matrix form, they are, in the Cartesian basis... 

Let us consider the propagation of electromagnetic waves with both fields nonzero E O and B 0. As usual, propagation is parallel to the Poynting vector G, defined in Eq. (17). Evidently, by definition, vector G is perpendicular to both fields E and B. Hence, there cannot exist components of the magnetic field B parallel to the instantaneous direction of propagation G. 

We see [with the definition of the magnetic field adopted in Eq. (1.1)] that the electric and magnetic fields are two mutually perpendicular vector fields with the same amplitude. Hence, the contribution of each field to the radiation energy is, according to Eq. (1.12), the same. Using this fact and Eq. (1.27) we can write Eq. (1.12) for an infinite cavity as... 

Vector analysis. The author learnt vector analysis in a 1950 postgraduate course, based on the German book of 1932, Classical Electricity and Magnetism, by M. Abraham and R. Becker, published by Blackie and Sons, Glasgow. The book was written so that its definitions of scalar flux (flow in all directions) and of vector current (flow in one direction) fitted both hydrodynamics and electromagnetism. The same definitions were carried over unmodified into the scalar neutron fluxes and vector neutron currents of the nuclear power reactor. In electrochemistry, however, the term exchange current attaches to what is more properly described (see above) as a local, somewhat anisotropic, scalar flux. 

Electric and magnetic properties of microsystems. Definition of multipoles electrostatics of permanent multipoles interaction energies for two multipoles induced molecular multipoles interaction energies of induced multipoles. Tables of point groups tensor elements of multipoles vector elements of multipoles tensor elements of polarizabilities. 

In the integration over z we note that, by definition, the electric and magnetic field vectors vanish at z = and have their maximum impact values at the surface of the wall, z = 0. Hence we find that... 

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