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Conductivity of ground problem

  1. Feb 26, 2005 #1
    Hi, I'm stuck on this problem:

    Two solid hemispherical conducting electrodes each of radius r=a are pressed into the earth, curved surfaces down, such that the flat surfaces are flush with the (flat) earth's surface. Assume that the electrode separation (center to center) is d where d >> a. We wish to measure the electrical conductivity of the ground from a measurement of the current I flowing between the electrodes. The two electrodes are connected above ground by a battery and a series ammeter, which completes the circuit through the earth. Assuming the earth is a homogeneous conductor with conductivity [tex]\sigma[/tex], find an expression for [tex]\sigma[/tex] in terms of the measured current and the given geometry. [Hints: Consider first: whole spheres immersed in a conducting medium. Let the two spheres have charge Q and -Q respectively and find the potentials of each sphere, and the capacitance of the pair.]

    I don't even understand the hint; why do I need to look at whole spheres and how does capacitance come into play here. Please help!! Thanks.
  2. jcsd
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