1. Analogy Principle

The resistance R and capacitance C of a system in a medium with resistivity ρ and permittivity ε are related by the equation:

R * C = ρ * ε

2. Determine Capacitance (C)

For two spheres of radius a separated by a large distance, the potential difference ΔV for a charge Q is:

ΔV = V₁ – V₂ = Q/(4πεa) – (-Q)/(4πεa) = Q/(2πεa)

So, Capacitance C = Q / ΔV = 2πεa.

3. Calculate Resistance (R)

Using the relation from Step 1:

R = (ρε) / C

R = (ρε) / (2πεa)

R = ρ / 2πa