In the Schlumberger resistivity method, the separation of the current electrodes L is much larger than the separation a of the voltage electrodes. Suppose that the mid-point of the voltage pair is displaced by a distance x from the mid-point of the current electrode pair as shown in the figure. Show that, for (L - 2x) >> a, the apparent resistivity is given by: ρ = (π V (L^2 - 4x^2)^2)/(4 I a (L^2 + 4x^2)) (10 marks)
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