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IN-WATER ELECTRICAL MEASUREMENTS 13 <br />Spatial Comparisons of Electric Fields <br />A voltage profile was recorded for each of the <br />18 pairs of electrodes on a transect intercepting <br />their vertical centroids. For example, the voltage <br />profiles for spheres were measured along a line <br />connecting through their centers. It was actually <br />only necessary to measure half of the S-curve for <br />each pair of electrodes because the electrical loads <br />were balanced and exhibited the reversed geomet- <br />ric symmetry described previously. <br />The voltage profiles indicate how effectively an <br />electrode projects energy into the water. For exam- <br />ple, if the S-curve exhibits an abrupt curvature and <br />rapid dissipation of voltage in proximity to an <br />electrode, the resultant electric field will be spa- <br />tially limited to a small volume. Conversely, larger <br />electric fields are generated by electrodes that <br />exhibit more linear (less bent) S-curves. Thus, <br />voltage profiles offer a basis for comparing the size <br />of electric fields by correlating these data in some <br />consistent manner. <br />I chose to analyze the data by interpolating those <br />distances from the voltage profiles at which 50 and <br />80% of the applied voltage (25 and 40 volts) was <br />dissipated. These two distances provide informa- <br />tion regarding the relative curvature of the S-curve; <br />short distances imply abrupt curvatures and vice <br />versa. However, I found these distances awkward <br />to interpret and, therefore, arbitrarily selected the <br />15.2-cm (6-inch) sphere as a "reference" electrode <br />for comparison. Subsequently, ratios were calcu- <br />lated by dividing the two distances interpolated <br />from the individual voltage profiles by the corre- <br />sponding distances actually measured for the 15.2- <br />cm sphere: 8.4 cm at 509/b voltage and 35.7 cm at <br />80% voltage. The resulting distance ratios then <br />relate the rate at which the voltage changed for a <br />test electrode compared with that of the reference <br />sphere. This comparison method offers a technique <br />that can be extended to any electrode configuration. <br />Also, this comparison is independent of the magni- <br />tude of applied voltage; the technique is based only <br />on the measurement of a distance at a given per- <br />centage of applied voltage. <br />The two distance ratios calculated for each elec- <br />trode can be directly correlated with the levels of <br />voltage gradient generated in the water. For exam- <br />ple, the 500/6 voltage ratio indicates the relative <br />magnitude of the voltage gradient in proximity to <br />the electrode; a small ratio implies an electrode that <br />dissipates its voltage in a short distance and <br />thereby generates high voltage gradients. In con- <br />trast, the ratios calculated for the 80% voltage <br />provide an index relating to the expanse of the <br />horizontal electric field; a large ratio implies that a <br />significant level of voltage gradient extends a <br />greater distance from an electrode. Table 2 summa- <br />rizes these two distance ratios for the 18 electrodes <br />and ranks these ratios from the smallest to the <br />largest. This ranking allows the reader to system- <br />atically compare the relative magnitudes of voltage <br />gradients and the extent of the horizontal electric <br />field among the 18 electrode configurations. <br />For the 18 test electrodes, the highest voltage <br />gradient was produced by the 36-cm horizontal <br />loop, while the 45.7-cm vertical plate generated the <br />lowest. As predicted, the same two electrodes also <br />project the shortest and farthest electric fields. <br />Note that all the electrodes tested, with the excep- <br />tion of the vertical plates, display a high degree of <br />radial symmetry. This symmetry implies that these <br />electrodes can be rotated about their vertical axes <br />without significant changes in their voltage pro- <br />files. The vertical plates are not radially symmetric, <br />and therefore create asymmetric electric fields that <br />project their farthest on a transect normal to the <br />surface of the plate. The comparative rankings in <br />Table 2 are based upon the optimal voltage profiles <br />for the plates as measured normal to their surface. <br />Observe that the two rankings in Table 2 are not <br />consistent. This inconsistency is caused by the <br />unusual geometry of Wisconsin arrays. In proxim- <br />ity, the individual droppers of these arrays gener- <br />ate levels of voltage gradients characteristic of <br />individual cylinders. At greater distances, how- <br />ever, the group of droppers mutually interacts to <br />extend the electric field to a greater distance. The <br />shape of the S-curve is therefore significantly al- <br />tered from those curves generated by electrodes <br />having a single, continuous surface. <br />Voltage Profiles <br />The voltage profiles for the 18 electrodes are <br />grouped according to their basic configuration <br />(spheres, cylinders, loops, Wisconsin arrays, and <br />vertical plates) and presented in Figs. 12 through <br />17. The empirical data for spheres and cylinders <br />were fit to known mathematical expressions (No- <br />votny and Priegel 1974), and statistical correla- <br />tion coefficients of greater than 0.995 were <br />achieved. There are no mathematical expressions <br />derived from electrical field theory for the loops, <br />Wisconsin arrays, and vertical plates, and I present <br />only the raw data in Figs. 14 through 17. All graphs <br />are presented to the same scaling to allow compari- <br />sons among the six groups.