Force electromagnetic Lorentz

Lorentz force. The Lorentz force is the product of the charge by the apparent potential, which amounts to saying that this force is the sum of forces exerted by the simultaneous action of an electric field E and of an electromagnetic induction field B on a charge Q moving with a velocity u. 

Figure 16 (a) Thermocapillary (Marangoni) forces M(+) or M(-) (b) electromagnetic (Lorentz) forces E, resulting from interaction of current (c) buoyancy forces B, resulting from density differences caused by temperature... 

M. Rambaut and J. P. Vigier, Ampere forces considered as collective non-relativistic limit of the sum of all Lorentz interactions acting on individual current elements Possible consequences for electromagnetic discharge stability and Tokamak behavior, Phys. Lett. A 148(5), 229-238 (1990). 

Figure 6. Illustrating electromagnetic action of the Lorentz force in a current-carrying conductor.

Taking this model for astrophysics further by postulating a Beltrami field morphology to electromagnetics, Chandrasekhar and Woltjer [15] posited that similar Lorentz force-free fields might exist which are quantified by the relation... 

Another type of electromagnetic actuator is shown in Fig. 8 c. It consists of a deflectable membrane having a metal conductor and a external permanent magnet. A current applied to the conductor perpendicular to the magnetic field generates the Lorentz force. 

The classical electromagnetic force acting on a particle of charge q is the Lorentz force (in Gaussian units)... 

To quantize the dynamics of the particles first requires that we express the velocities of the particles in terms of canonical momenta. In the presence of electromagnetic fields, the canonical momenta are not merely m dx-Jdt). Rather, in order to incorporate Lorentz s velocity-dependent forces into Hamilton s formulation of classical mechanics, the canonical momenta are given by [2]... 

The Lorentz force F on a particle of charge q in an electromagnetic field is... 

Table G Definitions of the Electric Field E, the (Di)electric Polarization P, the Electric Displacement D, the Magnetic Field H, the Magnetization M, the Magnetic induction or flux density B, statement of the Maxwell equations, and of the Lorentz Force Equation in Various Systems of Units rat. = rationalized (no 477-), unrat. = the explicit factor 477- is used in the definition of dielectric polarization and magnetization c = speed of light) (using SI values for e, me, h, c) [J.D. Jackson, Classical Electrodynamics, 3rd edition, Wiley, New York, 1999.]. For Hartree atomic u nits of mag netism, two conventions exist (1) the "Gauss" or wave convention, which requires that E and H have the same magnitude for electromagnetic waves in vacuo (2) the Lorentz convention, which derives the magnetic field from the Lorentz force equation the ratio between these two sets of units is the Sommerfeld fine-structure constant a = 1/137.0359895...

Theory of the dielectric function. The discussion of absorption properties of astrophysically relevant solids is frequently based on the classical Lorentz model for dielectric materials. This assumes that the electrons and ions forming the solid matter are located at fixed equilibrium positions in the solid, determined by internal forces. An applied electromagnetic field shifts the charged particles, labeled by... 

Figure 9.3. Operation of non-contact transducer performance. (A) Magnetostrictive and (B) electromagnetic type, (a) The sampie, wrapped in a soienoid, is piaced inside a magnetic fieid. (b) Lorentz forces generated on the sampie surface. DMF — direction of the magnetic fieid and S — soienoid. (Reproduced with permission of Eisevier, Ref [16].)...

The first achievement of the study of Holas and March [99] is to establish the differential form of the above virial theorem [their Eq. (2.15)]. Again, as in the zero field case treated above, this differential virial theorem is interpreted as a force-balance equation. The well-known Lorentz force of electromagnetism then appears quite naturally in this equation. 

We have performed numerical experiments using a three dimensional relativistic kinetic electromagnetic particle-in-cell code The code works from first principles by solving the Lorentz force equation for the particles and the Maxwell s equations for the electromagnetic fields. 

The second effect to be considered is the deflection of the weakly charged air flow by the electromagnetic field through the Lorentz force. The corresponding drag coefficients are (Hong and Lindzen, 1976)... 

The Lorentz force coupled with the Ampere law and the Faraday law leads to the balance of electromagnetic momentum2 which involves the (divergence of) electromagnetic (Maxwell) stress. The isotropic limit of this stress is the electromagnetic pressure... 

The joint action of pinning and Lorentz forces on vortex chain depends on the geometrical symmetry of the nanostructure. For the SMN of N-type the vortex chain is located in the center of N layer and the pinning force obstructs the vortex penetration inside the S layer. As bias current flows through the superconducting parts of the sample, dissipative processes are absent and the resistive transition is sharp (Fig. 1). For S-type nanostructures, vortex chain nucleates inside the central superconducting layer. Electromagnetic interaction between vortices and bias current leads to dissipation, it follows that in the central layer the sample resistance is not suppressed completely and the resistive transition becomes wider. 

The remaining parts of the lagrangian L describe the free field and fi-ee particles, and are not needed here. The requirements of V are that under lagrangian variation of the fields (for fixed partiele variables) it should contribute the appropriate terms to the Maxwell equations, and that variation of the particle variables (for a fixed electromagnetic field) gives the Lorentz force on the particles. 

---