Lorentz force law

The Lorentz Force Law can be used to describe the effects exerted onto a charged particle entering a constant magnetic field. The Lorentz Force Fl depends on the velocity v, the magnetic field B, and the charge of an ion. In the simplest form the force is given by the scalar equation [3,4,70,71]... 

How does the topology of the situation affect the explanation of an effect A typical previous explanation [44] of the Aharonov-Bohm effect commences with the Lorentz force law ... 

Furthermore, the U(l) Lorentz force law, Eq. (8), can hardly apply in this situation because the solenoid is electrically neutral to the test electrons and therefore E = 0 along the two paths. Using the definition of B in Eq. (5), the force law in this SU(2) situation is... 

The theoretical content of classical electrodynamics can be summarized by the Lorentz force law and Maxwell s equations. The Lorentz force law describes the force on a charge q moving with velocity v in the presence of an electric field E and a magnetic field B ... 

An ion of mass m and charge q travelling with a velocity v in an electric field with strength E and a magnetic field with flux density B experiences a force F defined by the Lorentz force law. This equation can be combined with Newton s laws to yield the acceleration a as... 

Two fundamental equations of classical physics provide convenient mathematical summaries of these experimentally observed effects, namely, Newton s Second Law of Motion and the Lorentz Force Law, written here as they apply to an ion of mass niijjn (kg) and charge qjj (coulombs C) ... 

All commonly used charged-particle analysers use electric and magnetic fields to apply a force on charged particles (electrons, and positive and negative ions). The relationship between force, mass, and the apphed fields is described by using two basic equations, namely Newton s second law and the Lorentz force law ... 

Maxwell s equations, which were first presented in 1864 and published in 1865 [40], completely describe the classical behavior of electric and magnetic fields and — supported by the Lorentz force law — their interaction with charged particles and currents. In Gaussian units their differential form is given by... 

It cannot be overemphasized that by specification of the action Stot the dynamics of both the electrodynamic and the material degrees of freedom, i.e., the gauge field and the particles x, is completely determined. The equations of motion for the gauge field are given by Eq. (3.198) and are recovered to be the inhomogeneous Maxwell equations. The equations of motion for the particles are given by Eq. (3.202) and comprise the familiar Lorentz force law. 

Unit conversion among magnetic properties depends on the dimensions used for the magnetic field, B. In the Gaussian and atomic units systems, electric fields and magnetic fields have the same dimensions, since the Lorentz force law is F (E -I- V X B/c). For these, Eq. [34] is valid for the conversion from atomic to Gaussian units. For S.I. units, where F = q(E -1- v x B), the conversion factor, F, is slightly different from Eq. [34] ... 

Furthermore, the key factor in successful HH cells (pot operations) is to predict and maintain MHD stability. This leads to the characterization of the internal MHD flow using Navier-Stokes equation of motion and Maxwell s equations, including of charge distribution, Faraday s law of induction. Ohm s law, Lorentz force law, Pcasson s equation, and even LaHace s equation. The set of these laws and equations constitute the MHD expressions. 

Magnetic Sector mass filters are based around the fact that an ion passing through a magnetic field (B) applied perpendicular to the ions trajectory will experience a deflection such that the trajectory follows an arc of some radius (r) dependent on the ions m/q ratio and velocity (v). This is indicated in Relation 4.9 as derived from the Lorentz force law. This is sometimes referred to as momentum filtering. 

It is not superfluous to point out that the relationship between wave-mechanical frequency and mechanical energy assumed here is hypothetical throughout, since we know that already the Lorentz force law, which regulates the influence of fields on matter, is replaced by something completely different, namely the wave equation. 

---