Momentum with electric force

In contrast to B sectors, E sectors utilize the component of Equation 3.27. Such instm-ments select ions according to their kinetic energy rather than momentum (as in B sectors). The radius of the circular ion path formed in the static electric sector can be derived by combining centrifugal force (Equation 3.28) with electric force, similar to Equation 3.29 but by replacing with Fg, to give ... 

Because the atoms in a vapor are electrically neutral, they caimot be manipulated by electric fields. However, because many of these atomic species have intrinsic angular momentum, they also have magnetic moments. Now, it is well known that a uniform magnetic field acting on an atom with magnetic moment p. caimot produce translational motion however, a nonumform field H(x can give rise to a force... 

The physical basis of the Raman effect is related to deformation of electron shells of molecules in an electric field E determined by the molecular polarisability a. Because the laser beam can be considered an oscillating electromagnetic wave with the electrical vector E and a frequency v0 it induces during interaction with the sample the electric dipole momentum P = aE. This momentum is the driving force of the deformation of the electronic shells of the molecules. Because this deformation is periodical, the molecular dipoles begin to vibrate with a characteristic frequency vm. 

Since we have a system subjected only to internal forces, and the motion takes place in a plane, the angle variable w2, associated with the total angular momentum, occurs in the Fourier representation of the electric moment with the factor 1 only (as was shown generally in 17). We can see this also directly, from the nature of the expressions for the angle variables. These are ... 

Let us estimate the electroosmotic velocity produced in a fine circular capillary by a uniform electric field applied along the axis as in Fig. 6.5.1. If the surface is assumed to be negatively charged, then the flow will be in the direction of the cathode, as shown. With the electric body force per unit volume given by fg = pgE, the momentum equation (Eq. 3.1.8) may be written... 

Aerosols can experience external influences induced by forces other than electrical or gravitational fields. For example, more than a century ago it was observed by side illumination that next to a heated object there is a layer containing practically no aerosol particles. The thickness of this layer was found to increase with the temperature of the object. In our discussion so far, we have assumed that the fluid in which our particles are suspended is homogeneous without temperature or gas concentration gradients, and so on. Under these conditions there is no preferential direction for the bombardment of the particle by fluid molecules. However, when there are gradients in the fluid temperature, concentration, and so on, there are differences in momentum imparted to a particle by molecules coming from different directions, producing a directional preference in the Brownian diffusion. 

In NaGd02 Eu " the Dd- I 2 emission transition dominates, but other lines are also present. The Eu case is so illustrative, because the theory of forced electric-dipole transitions [8] yields a selection rule in case the initial level has J - 0. Transitions to levels with uneven J are forbidden. Further J = O->J = 0is forbidden, because the total orbital momentum does not change. This restricts the spectrum to D()- Fi, present as magnetic-dipolc emission, but overruled by the forced electric-dipole emission,... 

In the momentum Equation 20, we again neglect accelerations, and use the coulomb force Equation 29 for the applied force on ions and electrons, with the electric field given by Poisson s Equation 28. That is,... 

Thus, in order to solve the hydrodynamic problem of liquid motion in view of the change of 2 at the interface, we should first And out the distribution of substance concentration, temperature and electric charge over the surface. These distributions, in turn, are influenced by the distribution of hydrodynamic parameters. Therefore the solution of this problem requires utilization of conservation laws - the equations of mass, momentum, energy, and electric charge conservation with the appropriate boundary conditions that represent the balance of forces at the interface the equality of tangential forces and the jump in normal forces which equals the capillary pressure. In the case of Boussinesq model, it is necessary to know the surface viscosity of the layer. From now on, we are going to neglect the surface viscosity. 

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