A Two Metal Objects Are Embedded In Weakly Conducting Material

(a) Two metal objects are embedded in weakly conducting material of conductivity a (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 I 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 V(t) = V0e –t/τ, and find the time constant, τ, in terms of ε0 and σ.

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