Dipoles electric field

When in motion, the diffnse electrical donble-layer aronnd the particle is no longer symmetrical and this canses a rednction in the speed of the particle compared with that of an imaginary charged particle with no donble-layer. This rednction in speed is cansed by both the electric dipole field set np which acts in opposition to the applied field (the relaxation effect) and an increased viscons drag dne to the motion of the ions in the donble-layer which drag liqnid with them (the electrophoretic retardation effect). The resnlting combination of electrostatic and hydrodynamic forces leads to rather complicated eqnations which, nntil recently, conld only be solved approximately. In 1978, White and O Brien developed a clever method of nnmerical solntion and obtained detailed cnrves over the fnll range of Ka valnes (0 °°)... 

So now we have the question poased in an interesting form. There are two quite different kinds of antennas, both of which produce electric dipole fields, but different Lorenz potentials, one emphasizing the vector potential and the other, the scalar potential. In a classical electromagnetic sense, one cannot distinguish these two cases by measurements of the fields (the measurable quantities) at distances away from the source region. The gauge invariance of QED implies the same in quantum sense. 

So our choices of the two antennas is not unique for separately emphasizing the Lorenz vector and scalar potentials. All that is required is for the two to have the same exterior fields (say, electric dipole fields, or more general multipole fields) with different potentials (related by the gauge condition). In a classical electromagnetic sense, these antennas cannot be distinguished by exterior measurements. This is a classical nonuniqueness of sources. In a QED sense, the same is the case due to gauge invariance in its currently accepted form. 

The first successful electric resonance experiment was reported by Hughes [48] who studied the CsF molecule, an appropriate beam being produced from a hot oven. He used both A and B electric dipole fields, separated by a homogeneous electric C field combined with a radio frequency electric field at right angles to the static field. In order to understand both the deflection and state selection in the dipole fields, as well as the electric resonance spectrum, we first consider the details of the Stark effect. 

The first order term of Eq. (8) is reduced to the field r ), the electric dipole field, whereas the second order term, linear with the parameter order x = a/X, is the sum of tire fields ( >, ) and ( >, ), respectively the electric quadrupole and the magnetic dipole fields. The surface nonlinear polarization of the form of Eq. (3) is now a series expansion with respect to the parameter x = a/X too. Its general expression is ... 

We now turn to the problem of the SU(2) quantum phase of multipole radiation. As a particular example of some considerable interest, we investigate the electric dipole field. All other types of the multipole radiation can be considered in the same way. 

Atomic Polarization Fields Ionic Fields Electric Dipole Fields The Helmholtz Planes Diffuse Double Layer Compact Double Layer Potential Transients Constant Current Constant Potential Faradaic Processes Non-Faradaic Ideal Polarizable... 

The threshold condition for collective emission (superradiance) or maser action (gain in the medium exceeding the losses) is much lower for Rydberg atoms than it is for the same number density of atoms in low n states. To obtain an order of magnitude estimate for the point at which collective fects occur we estimate the amplitude of the electric dipole field E radiated by an atom at a distance corresponding to a neighbouring atom. That is, if we let L represent a linear dimension in the sample which contains N atoms,... 

The transition strength for the change from any initial quantum state i to final state /, by way of interaction with a photons electric dipole field, is proportional to (Eq. 6.10)... 

What if one molecule has a dipole moment and the other does not In that case, the electric field of the polar molecule can induce a dipole moment in the other. For example, N2 has no permanent electric dipole field. When dissolved in H2O, however, the dipole moment of the H2O can cause the charges in the N2 to separate a little bit, leading to an induced dipole moment, as illustrated in Fig. 10.11. 

The intensity of the fluorescence emitted into the direction e against the quantization axis is obtained as the product of the emission rate dn/dt of individual photons and the appropriate angular distribution of the electric dipole field. In the far field zone at a distance p x one obtains... 

Figure 8.2.7 Schematic diagram of electron dipole scattering in front of a surface. The long-range electric field of the electron (electric field lines marked by dashed lines) interacts with the oscillating electric dipole field (lines of equipotential are marked dot-dashed) because of a surface vibration.

All the remarks concerning the behaviour of the fields in the near and wave zone which we made in section 2.7 in connection with the electric dipole fields apply in the magnetic dipole case if we make the interchanges... 

The reverse problem (knowing potential calculation is easier than calculating the field strength since the former is a scalar value, whereas the latter is of vector quality). 

The solutions can be labelled by their values of F and m.p. We say that F and m.p are good quantum. num.bers. With tiiis labelling, it is easier to keep track of the solutions and we can use the good quantum numbers to express selection rules for molecular interactions and transitions. In field-free space only states having the same values of F and m.p can interact, and an electric dipole transition between states with F = F and F" will take place if and only if... 

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

A related phenomenon with electric dipoles is ferroelectricity where there is long-range ordermg (nonzero values of the polarization P even at zero electric field E) below a second-order transition at a kind of critical temperature. 

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

A very weak peak at 348 mn is the 4 origin. Since the upper state here has two quanta of v, its vibrational syimnetry is A and the vibronic syimnetry is so it is forbidden by electric dipole selection rules. It is actually observed here due to a magnetic dipole transition [21]. By magnetic dipole selection rules the A2- A, electronic transition is allowed for light with its magnetic field polarized in the z direction. It is seen here as having about 1 % of the intensity of the syimnetry-forbidden electric dipole transition made allowed by... 

The oscillating electric dipole density, P (the polarization), that is induced by the total incident electric field,... 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

When monochromatic radiation falls on a molecular sample in the gas phase, and is not absorbed by it, the oscillating electric field E (see Equation 2.1) of the radiation induces in the molecule an electric dipole which is related to E by the polarizability... 

In the context of discussion of the Raman effect, Equation (5.43) relates the oscillating electric field E of the incident radiation, the induced electric dipole fi and the polarizability a by... 

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

Applications. Molecules couple to an electromagnetic field through their electric dipoles, so only those having a permanent dipole moment exhibit significant rotational spectra. For such species, microwave spectroscopy yields highly precise moments of inertia and details of centrifugal... 

Barium titanate [12047-27-7] has five crystaUine modifications. Of these, the tetragonal form is the most important. The stmcture is based on corner-linked oxygen octahedra, within which are located the Ti" " ions. These can be moved from their central positions either spontaneously or in an apphed electric field. Each TiO octahedron may then be regarded as an electric dipole. If dipoles within a local region, ie, a domain, are oriented parallel to one another and the orientation of all the dipoles within a domain can be changed by the appHcation of an electric field, the material is said to be ferroelectric. At ca 130°C, the Curie temperature, the barium titanate stmcture changes to cubic. The dipoles now behave independentiy, and the material is paraelectric (see Ferroelectrics). 

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