Lorentz force electromagnetic field

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. 

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... 

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 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. 

The vector product occurs in the force law for a charged particle moving in an electromagnetic field. A particle with charge q moving with velocity v in an electric field E and a magnetic induction field B experiences a Lorentz... 

These models solve for the electron s motion in the presence of the electromagnetic field as a driving force. From this, it is possible to write an expression for the polarization induced in the medium and from that to derive the dielectric constant. The Lorentz model for dielectrics gives the relative real and imaginary parts of the dielectric constant as... 

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. 

The force F of an electromagnetic field on a particle with charge q and called the Lorentz force and is given as mass m is... 

A similar relation holds for atoms in optical fields where the field frequency (0 is off resonance with the atomic frequency coq. In an electromagnetic field the Lorentz force on an atom in a dilute medium (refractive index n l, - n-l 1) is [13.15]... 

---