Maxwell current

M E. Davis, I.E. Maxwell, Current Opinion in Solid State Materials Science, 1 (1996) 55. 

A three-dimensional time-dependent model has been developed by Ma et al. (1998) to solve for the electric field, charge density, and Maxwell current. The last quantity is influenced primarily by the spatially anisotropic tensor conductivity in the ionosphere. Maxwell s equations for the transient fields propagating into the ionosphere are reduced to two equations. If p is the charge density (C/m ), q the dielectric constant (C /N m ), the permeability (N/A ), 0 the conductivity tensor (S/m), and E the electric field (V/m), then the wave equation in SI imits becomes... 

Maxwell current density Mathematical curl of the magnetic field vector H, eqnal to the vector sum of all current densities, which in the atmosphere is usually limited to conduction, convection, diffusion, lightning, and displacement cnrrent terms. 

Currently the charts used most often for this purpose are those published by the API. (Maxwell and Bonnel charts) from the Technical Data Book (see Chapter 4). 

Fig. 2.1.3 A pair of saddle coils creates an x or y gradient (left), a pair of Maxwell coils creates a z gradient (right). The arrows on the coils indicate the current direction, the circles with...

Ionic current density maps can be recorded with the aid of the pulse sequence shown in Figure 2.9.2. The principle of the technique [48-52] is based on Maxwell s fourth equation for stationary electromagnetic fields,... 

E and B are the fundamental force vectors, while P and H are derived vectors associated with the state of matter. J is the vector current density. The Maxwell equations in terms of E and B are... 

By interpreting the term in brackets as the total current density the inhomogeneous Maxwell equation (2) is also written as... 

A schematic of an eddy-current damper is shown in Fig. 10.6. A copper block with resistivity p is under the influence of the magnetic field 6 of a permanent magnet. The relative motion of the magnet and the copper block in the X direction causes a force in the -x direction. By solving Maxwell s equation numerically, Nagaya (1984) calculated the force to be... 

The space-charge current density in vacuo expressed by Eqs. (3) and (4) constitutes the essential part of the present extended theory. To specify the thus far undetermined velocity C, we follow the classical method of recasting Maxwell s equations into a four-dimensional representation. The divergence of Eq. (1) can, in combination with Eq. (4), be expressed in terms of a fourdimensional operator, where (j, 7 p) thus becomes a 4-vector. The potentials A and are derived from the sources j and p, which yield... 

Before turning to the details of the present analysis, we describe and compare the main features of some of the modified and extended theories that have been proposed and elaborated on with the purpose of replacing Maxwell s equations. This description includes a Proca-type equation as a starting point. Introducing the 4-potential, 4M = ( , / ) and the 4-current the latter equation can be written as... 

Bartlett and Corle [46] proposed modification of Maxwell s equations in the vacuum by assigning a small nonzero electric condictivity to the formalism. As pointed out by Harmuth [47], there was never a satisfactory concept of propagation velocity of signals within the framework of Maxwell s theory. Thus, the equations of the latter fail for waves with nonnegligible relative frequency bandwidth when propagating in a dissipative medium. To resolve this problem, a nonzero electric conductivity ct and a corresponding current density... 

Chubykalo and Smirnov-Rueda [2,56] have presented a renovated version of Hertz theory, that is in accordance with Einstein s relativity principle. For a single point-shaped charged particle moving at the velocity v, the displacement current in Maxwell s equation is modified into a convection displacement current ... 

Noether charges proportional to the remaining right-hand-side terms do not disappear, leaving one of the Lehnert equations [7-10]. Lehnert introduced the vacuum charge empirically. Lehnert and Roy [10] have given clear empirical evidence for the existence of vacuum charge and current. The latter appears in the 0(3) Ampere-Maxwell law, which in field-matter interaction is... 

The first example of a vacuum current was introduced by Maxwell in order to make the equations of electrostatics and magnetostatics self-consistent. The second examples were introduced in 1979 [7] by Lehnert, and 0(3)... 

Equations (573) have overall 0(3) symmetry, and have the same structure as the Maxwell-Heaviside equations with magnetic charge and current [3,4]. From Eqs. (573), we obtain the wave equation... 

In the received opinion [5], these are the vacuum Faraday law and Ampere-Maxwell law, respectively. The vacuum charges and currents are missing in the received opinion. Nevertheless, solving Eq. (625) numerically is a useful computational problem with boundary conditions stipulated in the vacuum. The potentials and fields are related as usual by... 

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