Moving Current Dipole

The propagation of the action potential signal through tissue is occurring with an accompanying low-pass filtering effect (Section 6.4.1). 

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Figure 6.10 Moving current dipole ( ) with fixed position unipolar recording electrode.

A technically ideal (Section 6.2.3) current dipole with constant moment moves with constant velocity along the jc-axis in an ideal volume. Figure 6.10. The monopolar and bipolar potentials are calculated at a fixed point on the y-axis at distance 5Lcc and lOLcc. The monopolar and bipolar potentials are calculated using Eq. (6.11) with Ip = 2(KX)tc. 

Figure 6.11 Unipolar potentials from a current dipole moving along the horizontal x-axis. Dipole length is L c) the unit of the x-axis is L c- The recording electrode is at distance SL c and lOLcc (a) horizontal dipole orientation, biphasic waveforms, and high spatial resolution (b) vertical dipole orientation, monophasic waveforms, and largest signal amplitude of...

Though the ESR Hamiltonian is typically expressed in terms of effective electronic and nuclear spins, it can, of course, also be derived from the more fundamental Breit-Pauli Hamiltonian, when the magnetic fields produced by the moving nuclei are explicitly taken into account. In order to see this, we shall recall that in classical electrodynamics the magnetic dipole equation can be derived in a multipole expansion of the current density. For the lowest order term the expansion yields (59)... 

The magnetic dipole moment p can be defined from a constant current I moving in a circular loop. The magnitude of p is given by... 

Polar molecules display the property that they can be oriented along an electric field dipolar polarization phenomenon). In the absence of this phenomenon, dipoles are orientated at random and molecules submitted to Brownian movement only. In the presence of a continuous electric current, aU the dipoles are lined up together in the same direction. If submitted to an alternating current, the electric field is inversed at each alternance with a subsequent tendancy for dipoles to move together to follow the field. Such a characteristic induces stirring and friction of molecules which dissipates as internal homogeneous heating (Scheme 21). 

Endo et al. (1992) measured the optical transmission and the polarity-reverse current during the polarity reversion of a side chain ferroelectric liquid crystalline polymer. It was found that both parameters reached peak values at the same time. It was concluded that the rigid core of the side groups responsible for birefringence moves simultaneously with the dipole moment reversion and the latter contributes to the polarity reversion current. The FTIR experiment suggested that the backbone moves when the polarity is reversed. 

We start from the first pair of Maxwell equations connected with electric charges moving in vacuum. Let vector J be the electric current density produced by these charges. In the case of a polar medium, positive (q) and negative (—q) charges of each dipole are bound one to the other. Therefore we may represent the complex power (244) as... 

A phenomenon called dielectrophoresis has been used to pattern a variety of cell types on 2D substratesand more recently in 3D culture constructs. Unlike electrophoresis where charged species move in an applied electric field due to Coulombic forces (F = qE), dielectrophoresis capitalizes on the ability of a cell to become polarized when placed in an electric field. Dielectrophoresis is most often used in conjunction with dtemating current (AC) electric fields since AC fields eliminate electrophoretic movement, and have less physiological impact on cells than direct current (DC) fields. When a cell is placed in an AC field, the magnitude and polarity of the induced dipole depend on the frequency of the applied field and the conductivities of the cell and the surrounding medium, described by the equation... 

In a manner analogous to TMA and DMA, a specimen can be subjected to a constant or oscillating electric field rather than a mechanical stress during measurements. Dipoles in the material will attempt to orient with the electric field, while ions, often present as impurities, will move toward the electrode of opposite polarity. The resulting current flow is similar in nature to the deformation brought about by mechanical tests and represents a measure of the freedom of charge carriers to respond to the applied field. The specimen is usually presented as a thin film between two metal electrodes so as to form a parallel plate capacitor. Two types of test can be performed. 

In an ideal insulating material there are no free electric charges that can move continuously in the presence of an electric field, so no current can flow. In the absence of any electric field, the bound positive and negative electric charges within any small volume element du will, in the simplest case, be distributed in such a way that the volume element does not have any electric dipole moment. If, however, an electric field is applied to this volume element of the material, it will cause a change in the distribution of charges, so that the volume element acquires an electric dipole moment... 

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