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We study the electric potential and field produced by disordereddistributions of charge to see why clumps of charge do not produce largepotentials or fields. The question is answered by evaluating the probabilitydistribution of the electric potential and field in a totally disordered systemthat is overall electroneutral. An infinite system of point charges is calledtotally disordered if the locations of the points and the values of the chargesare random. It is called electroneutral if the mean charge is zero. In onedimension, we show that the electric field is always small, of the order of thefield of a single charge, and the spatial variations in potential are what canbe produced by a single charge. In two and three dimensions, the electric fieldin similarly disordered electroneutral systems is usually small, with smallvariations. Interestingly, in two and three dimensional systems, the electricpotential is usually very large, even though the electric field is not: largeamounts of energy are needed to put together a typical disordered configurationof charges in two and three dimensions, but not in one dimension. If the systemis locally electroneutral--as well as globally electroneutral--the potential isusually small in all dimensions. The properties considered here arise from thesuperposition of electric fields of quasi-static distributions of charge, as innonmetallic solids or ionic solutions. These properties are found indistributions of charge far from equilibrium

Attenuation of the Electric Potential and Field in Disordered Systems