Potential field strength

Fig. 7.3. LDOS at n = 1 site of 100-atom chain. As held increases, semi-elliptical shape is dominated by linear potential. Field strengths are as indicated. Reprinted from Davison et al (1997) with permission from the Institute of Physics.

Absolute potential at the electrode surface Overall conversion related yield Absolute potential of the bulk solution phase Absolute potential at the plane of closest approach of cations Potential field strength Rotation rate... 

Unless extremely high potentials are to be used, the intense electric fields must be formed by making the radius of curvature of the needle tip as small as possible. Field strength (F) is given by Equation 5.1 in which r is the radius of curvature and k is a geometrical factor for a sphere, k = 1, but for other shapes, k < 1. Thus, if V = 5000 V and r = 10 m, then, for a sphere, F = 5 x 10 V/m with a larger curvature of, say, Iff m (0.1 mm), a potential of 500,000 V would have to be applied to generate the same field. In practice, it is easier to produce and apply 5000 V rather than 500,000 V. 

When corona occurs, current starts to flow in the secondary circuit and some dust particles are precipitated. As potential is increased, current flow and electric field strength increase until, with increasing potential, a spark jumps the gap between the discharge wire and the collecting surface. If this "sparkover" is permitted to occur excessively, destmction of the precipitator s internal parts can result. Precipitator efficiency increases with increase in potential and current flow the maximum efficiency is achieved at a potential just short of heavy sparking. 

Measurement by Electromagnetic Effects. The magnetic flow meter is a device that measures the potential developed when an electrically conductive flow moves through an imposed magnetic field. The voltage developed is proportional to the volumetric flow rate of the fluid and the magnetic field strength. The process fluid sees only an empty pipe so that the device has a very low pressure drop. The device is useful for the measurement of slurries and other fluid systems where an accumulation of another phase could interfere with flow measurement by other devices. The meter must be installed in a section of pipe that is much less conductive than the fluid. This limits its appHcabiHty in many industrial situations. 

The theory and appHcation of SF BDV and COV have been studied in both uniform and nonuniform electric fields (37). The ionization potentials of SFg and electron attachment coefficients are the basis for one set of correlation equations. A critical field exists at 89 kV/ (cmkPa) above which coronas can appear. Relative field uniformity is characterized in terms of electrode radii of curvature. Peak voltages up to 100 kV can be sustained. A second BDV analysis (38) also uses electrode radii of curvature in rod-plane data at 60 Hz, and can be used to correlate results up to 150 kV. With d-c voltages (39), a similarity rule can be used to treat BDV in fields up to 500 kV/cm at pressures of 101—709 kPa (1—7 atm). It relates field strength, SF pressure, and electrode radii to coaxial electrodes having 2.5-cm gaps. At elevated pressures and large electrode areas, a faH-off from this rule appears. The BDV properties ofHquid SF are described in thehterature (40—41). 

Field Strength Whereas the applied potential or voltage is the quantity commonly known, it is the field strength that determines behavior in an electrostatic field. When the current flow is low (i.e., before the onset of spark or corona discharge), these are related by the following equations tor two common forms of electrodes ... 

Here / is induced current, U is pipeline potential, and x is the position coordinate. With the locally constant field strength, E, it follows from Eqs. (23-5) and (23-6) ... 

The field strength, E, induced by grounding short-circuit currents in high-voltage overhead power lines or railway power lines, is basic in calculating the pipeline potentials (see Section 23.3.2). The field strength, E, follows from Refs. 2 and 13 ... 

To determine the pipeline potentials, the resultant induced field strengths have to be included in the equations in Section 23.3.2. Such calculations can be carried out with computers that allow detailed subdivision of the sections subject to interference. A high degree of accuracy is thus achieved because in the calculation with complex numbers, the phase angle will be exactly allowed for. Such calculations usually lead to lower field strengths than simplified calculations. Computer programs for these calculations are to be found in Ref. 16. 

The parameter E, which is called the diffusional field strength, arises only when the Dj values of the cation and anion differ appreciably when they are identical, E is zero. As a result of this field strength in the electrolyte, a diffusional potential difference 9 arises along the diffusion path from x = 0 to = 8 ... 

The ionic concentration gradients in the transition layer constitute the reason for development of the diffusion component E of electric field strength (the component arising from the difference in diffusion or mobihties between the individual ions). The diffusion potential between the solutions, 9 = - / can be calculated... 

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