Sphere monopole source

The conductance G of a superconducting hemisphere of radius a, half submerged in a halfinfinite homogeneous biomaterial and with a concentric half-spherical reference electrode 

In a real case with a metal electrode in an electrolyte solution, the electrode polarization impedance resulting from the surface layer is physically in series with the electrolytic resistance given by Eq. (6.1). Equation (6.1) shows that the electrolytic resistance is inversely proportional to radius a (or circumference 2Tca) of the electrode. However, the electrode polarization impedance is inversely proportional to a (surface area 2Tca ). Therefore, the influence of the electrode polarization can be made as small as wanted by increasing the sphere radius. Alternatively, by reducing the electrode radius sufficiently, it 

The resistance contribution of a finite hemispheric shell of radius r on the metal sphere of radius a is  

Injecting a current I into a hemisphere, the current density J in the tissue volume in radial direction is  

Notice that V is a voltage supplied by an external wire circuit, is a potential in space. 

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The cross section of a bar is proportional to its mass, thus there are efforts to build a 100-ton spherical resonant de-teetor, with high sensitivity and omnidirectional response. The sphere must be equipped with several transducers to detect the fundamental modes the quadrupole modes and the monopole mode (not sensitive to gravitational waves). Efforts are also being devoted to developing more efficient electronics systems (transducers and amplifiers) to achieve better sensitivity. Another major improvement foreseen is the increase of the bandwidth from the current few hertz to several tens of hertz. In this way, coincident runs could allow the determination of source position. 

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