(a) Two metal objects are embedded in weakly conducting material of conductivity σ (Fig....

(a) Two metal objects are embedded in weakly conducting material of conductivity σ (Fig. 7.6). Show that the resistance between them is related to the capacitance of the arrangement by

(b) Suppose you connected a battery between 1 and 2, and charged them up to a potential difference V₀. If you then disconnect the battery, the charge will gradually leak off. Show that and find the time constant, τ, in terms of ϵ₀ and σ.