Electrical sinusoidal electric fields

Figure Bl.5.2 Nonlinear dependence of tire polarization P on the electric field E. (a) For small sinusoidal input fields, P depends linearly on hence its hannonic content is mainly tiiat of E. (b) For a stronger driving electric field E, the polarization wavefomi becomes distorted, giving rise to new hannonic components. The second-hamionic and DC components are shown.

If an electric field, sinusoidally varying in time, is imposed on the gas, the force on the electrons, per unit mass, is... 

Fig. 6a. Schematic illustration of deformation measurement of PVA-PAA gel film in electric fields, b Deflection curves of PVA-PAA gel film under sinusoidally varied electric fields...

The strain in electric field-associated bending of a PVA-PAA gel is given by the equation g = 6DY/L2 (see Eq. 21). The strain depends on the electric power applied to the gel. Thus, the deflection increases as the thickness becomes small even if the electric power remains constant. The PVA-PAA gel rod of 1 mm diameter bends semicircularly within 1 s under both dc and ac excitation. An artificial fish with a PVA-PAA gel tail 0.7 mm thick has been designed, and it has been demonstrated that the fish swims forward at a velocity of 2 cm/sec as the gel flaps back and forth under sinusoidally varied electric fields (Fig. 13b). This prototype of a biomimetic actuator shows that translational motion may be produced using bending deformation [74],... 

The measurement of the Stark effect were carried out with the electric-field modulation technique at room temp, in vacuo (about 10 3 torr). A sinusoidal ac voltage (500 Hz) was applied between the A1 electrodes. Then, the change in transmittance induced by the applied electric field were measured with a phase-sensitive detector (NF Electronic Instruments LI-575A) at the fundamental frequency. 

Method involves placing a specimen between parallel plate capacitors and applying a sinusoidal voltage (frequencies ranging from 1 mHz to 1 MHz) to one of the plates to establish an electric field in the specimen. In response to this field, a specimen becomes electrically polarized and can conduct a small charge from one plate to the other. Through measurement of the resultant current, the dielectric constant and dielectric loss constant for a specimen can be measured. The sharp increases in both the dielectric constant and the dielectric loss constant during a temperature scan are correlated with the occurrence of Tg... 

In general, an electric field E (r) emitted from an isolated, fixed-amplitude dipole (i.e., no surfaces nearby) can be expanded as an integral over plane waves (with sinusoidal time dependence suppressed) as follows ... 

Consider a molecule placed in a sinusoidally varying electric field. For simplicity, we will assume that the field is linearly polarized. The Hamiltonian of the molecule is... 

A piezoelectric crystal is one whose dimensions change in an applied electric field. A sinusoidal voltage applied between two faces of the crystal causes it to oscillate. Quartz is the most common piezoelectric material. 

This equation describes a sinusoidal response at frequency, co, to the electric field component at co. This is the basis for the linear optical response. To calculate the optical properties of the Lorenz oscillator the polarization of the medium is obtained as... 

Figure 1. Fundamentals of ICR excitation. The applied magnetic field direction is perpendicular to the page, and a sinusoidally oscillating radiofrequency electric field is applied to two opposed plates (see upper diagrams). Ions with cyclotron frequency equal to ("resonant" with) that of the applied rf electric field will be excited spirally outward (top right), whereas "off-resonant" ions of other mass-to-charge ratio (and thus other cyclotron frequencies) are excited non-coherently and are left with almost no net displacement after many cycles (top left). After the excitation period (lower diagrams), the final ICR orbital radius is proportional to the amplitude of the rf electric field during the excitation period, to leave ions undetected (A), excited to a detectable orbital radius (B), or ejected (C).

Figure 1.11 Variation of the mixing index with the frequency for an electric field intensity of 4.24 105 V rrf1 for an AC sinusoidal (diamonds) and square (squares) electric fields [91] (by courtesy of RSC).

Figure 4.20 A sinusoidal electric field of angular frequency u> in a second-order nonlinear optical medium creates a polarization with component at 2tn( second-harmonic) and a steady (dc) component...

Figure 10 shows a typical measured homodyne waveform and the corresponding numerical fit (solid lines). The measured THz waveform exhibits both the fundamental ECDL difference frequency (Fig. 10(a)) and higher harmonics - predominantly the third harmonic (Fig. 10(b)). Multiple harmonic generation in THz photo-mixers has been previously reported [103], By fitting the observed waveform to a sum of harmonic sinusoidal functions, the amplitude and phase of the THz electric field can be determined separately for the fundamental and third harmonic. The solid line shows a numerical fit to the data. The fundamental extracted frequency, 0.535 THz, compares well to the expected frequency based on the frequency difference of the two ECDL. The extracted E field amplitudes and phases are 3.37 x 10 4 and 2.17 radians for 0.535 THz (Fig. 10(a)) and 5.61 x 10-5 and 3.94 radians for the 1.605 THz third harmonic, respectively (Fig. 10(b)). 

A simple thin film technique has been developed to measure the electrical properties of polyelectrolyte solutions under sinusoidal electric fields of 100-500 v/cm at frequencies of. 10-10 KHz. Ohmic heating is largely avoided by the rapid transfer of heat to the electrodes and by the high surface to volume ratios. The resulting temperature is not sufficient to damage the medium. Current and voltage wave forms are monitored directly so that dispersion and nonlinear phenomena of the medium can be viewed directly as functions of frequency, voltage, and concentration of the solution. Possible mechanisms for the observed phenomena are discussed. 

The discussion so far has been concerned with dielectrics in steady electric fields more commonly they are in fields that change with time, usually sinusoidally. This is clearly the case for capacitors in most ordinary circuit applications, but there are less obvious instances. For example, because electromagnetic waves have an electric field component it would be the case for dielectric resonators in microwave devices and also for fight passing through a transparent material. Fortunately, no matter how the field may vary with time, the variation can be... 

The values of the piezoelectric properties of a material can be derived from the resonance behaviour of suitably shaped specimens subjected to a sinusoidally varying electric field. To a good approximation the behaviour of the piezoelectric... 

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