Magnetic quantities

The external magnetic field is characterised by the vector of magnetic induction B(Bx By, Bz) which is interrelated with the vector of magnetic field strength H(HX, Hy, Hz) through a material constant—permeability p, viz. 

Here we have assumed a homogeneous isotropic material but in general the permeability is a second-rank tensor jt having 3x3 elements. The applied magnetic field is modified by the bulk magnetic properties of the substance and thus the magnetic field inside the sample becomes 

More exactly, for a non-homogeneous material a differentiation should be applied 

In a vacuum, the magnetisation vanishes and thus it holds true that 

Here a mean volume magnetic susceptibility has been introduced X = M/H 

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The dimensions of units in electricity and magnetism are the origin of much confusion. In the days when mechanical and thermal quantities were expressed in cgs, two different systems were introduced for the electrical and magnetic quantities. They are the esu (electrostatic units) and the emu (electromagnetic... 

The nonvanishing components of the tensors y a >--eem and ya >-mee can be determined by applying the symmetry elements of the medium to the respective tensors. However, in order to do so, one must take into account that there is a fundamental difference between the electric field vector and the magnetic field vector. The first is a polar vector whereas the latter is an axial vector. A polar vector transforms as the position vector for all spatial transformations. On the other hand, an axial vector transforms as the position vector for rotations, but transforms opposite to the position vector for reflections and inversions.9 Hence, electric quantities and magnetic quantities transform similarly under rotations, but differently under reflections and inversions. As a consequence, the nonvanishing tensor components of x(2),eem and can be different... 

The largest components of the tensors / and yare chiral. Furthermore, these components are larger than the chiral component of y ". Hence the strongest magnetic quantities are directly associated with the chirality of... 

As a particular example of materials with high spatial symmetry, we consider first an isotropic chiral bulk medium. Such a medium is, for example, an isotropic solution of enantiomerically pure molecules. Such material has arbitrary rotations in three dimensions as symmetry operations. Under rotations, the electric and magnetic quantities transform similarly. As a consequence, the nonvanishing components of y(2),eee, y 2)-een and y,2)jnee are the same. Due to the isotropy of the medium, each tensor has only one independent component of the xyz type ... 

We shall use mainly the cgs Gaussian system of units. This is a mixed system with electrical quantities measured in cgs electrostatic units (esu) and magnetic quantities measured in cgs electromagnetic units (emu). 

TABLE 3.3 Frequently Used Magnetic Quantities in the SI and the CGS System11... 

Chapter 1 is an introduction into some basic concepts of interest to more than one chapter, such as the definitions of basic magnetic quantities. Chapters 2-4 are devoted to the theory of magnetic nanostructures, 5 deals with the characterization of the structures, and 6-10 are devoted to specific systems. Applications of advanced magnetic nanostructures are discussed in 11-15 and, finally, the appendix lists and briefly discusses magnetic properties of typical starting materials. 

Magnetic quantities are defined in much the same way as electric quantities. The unit magnetic pole is such that two of them, one centimeter apart in a vacuum, repel each other with a force of one dyne. The strength of a magnetic field is taken to be equal to the force in dynes on a unit pole put in the field. 

Quantities and Units-Part 0 General Principles Units and Symbols Quantities and Units-Part 1 Space and Time Quantities and Units-Part 2 Periodic and Related Phenomena Quantities and Units-Part 3 Mechanics Quantities and Units-Part 4 Heat Quantities and Units-Part 5 Electricity and Magnetism Quantities and Units-Part 6 Light and Related Electromagnetic... 

In the context of attempts to use only units based on the SI system an alternative definition of atomic units was proposed. One starts from the SI system (with 4 basic units), and measures then mass, electric charge, action and quantities of the dimension of the dielectric constant of the vacuum in units of m, e, h, and 47reo respectively. On this way one arrives at the same Hamiltonian in atomic units, as following Hartree - as long as no magnetic quantities are involved. We must therefore reconsider the system of units, when we come to electrons in the presence of magnetic fields (section 2,10). 

For definitions of the concepts and magnetic quantities used here (the primary system of units in this chapter is CGS) and discussions of different magnet materials see other articles in this Handbook (Zijlstra 1982, Stablein 1989, Buschow 1988), also general textbooks on magnets (e.g., McCaig 1977, Burzo 1986). The textbook by Burzo has an exhaustive bibliography on the REPM, current as of 1985. 

As in the previous reviews, we put much emphasis on the dimensions of all used quantities. We work with the "Gauss cgs system" where electric and magnetic quantities have the same dimensions with respect to the three basic dimensions T, time M, mass and L, space. 

Two other important magnetic quantities, the magnetic induction, a vector quantity, B, and the magnetic field strength, a vector, H, are defined by reference to a solenoid, which is a cylindrical coil carrying an electric current. In a vacuum, the magnetic induction and magnetic field within the... 

Table A.2 Derived units (examples only the list can be continued, e. g. magnetic quantities). for electric and...

Gaussian units A system of units for electric and magnetic quantities based upon c.g.s. electrostatic and electromagnetic units. Although replaced by S1 units in most branches of science, they are, like Heavi-side-Lorentz units, still used in relativity theory and in particle physics. In Gaussian units, the electric and magnetic constants are both equal to unity. 

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