Monopolar sphere

The monopolar sphere is the most basic geometry in the sense that any electrode in an infinite homogeneous medium reverts to a symmetrical spherical geometry at... 

There are monopolar fluctuations of the net charge on the colloid and its surrounding solution there are dipolar fluctuations, the first moment of the ionic-charge distribution around the colloid as well as polarization of the colloid itself. Monopolar and dipolar fluctuations couple to create a hybrid interaction, d-m, again in the limit of the n = 0 sampling frequency at which the ions are able to fluctuate. The salt solution screens even the dipolar fluctuation the same way that the low-frequency-fluctuation term is screened in planar interactions. For dielectric spheres of radius a, ss whose incremental contribution to dielectric response is a =... 

Not only are there fluctuations in the electric fields that create the dipolar fluctuations of most van der Waals forces but there are also fluctuations in electric potential with concomitant fluctuations in the number density of ions and the net charge on and around these small spheres. Monopolar charge-fluctuation forces occur when ion fluctuations in the spheres differ from ion fluctuations in the medium. Perhaps it is better to say that these forces occur when ion fluctuations around the suspended particles differ from what they would have been in the solution in the absence of particles. To formulate these interactions, we allow the ionic population of the spheres to equilibrate with the surrounding salt solution and to exchange ions with that surrounding solution. Then we compare the ionic fluctuations that occur from the presence of the small spheres with those in their absence. To do this we must have a way to count the number of extra ions associated with each sphere compared with the number of ions in their absence. 

Accordingly, 99% of the total resistance is within a sphere of radius 100a, and 90% within a sphere of radius 10a. The resistance value measured with a small spherical monopolar electrode may therefore show good spatial selectivity. A concentric hemisphere is an equipotential surface, and the surface can therefore be covered by a thin metal sheet acting as one electrode. It is not a neutral electrode until r is large. As a neutral electrode, a hemispherical electrode with r oo is equal to an infinite area bottom plate at infinite distance (Figure 6.2). 

Figure 7.37 shows the monopolar impedanee spectrum measured with a thin insulated needle inserted in porcine living tissue. The 90% sensitivity zone is roughly a sphere of about 3 mm centered at the exposed needle tip. Above = 10 kHz the data are dominated by tissue properties, below 1 kFlz by electrode polarization impedance. 

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