# Conductivity of ground problem

1. Feb 26, 2005

### meteorologist1

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 $$\sigma$$, find an expression for $$\sigma$$ 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.