Two conductors of aribitary shape are embedded into an infinite homogenous poorly conducting medium with respectivity `rho` and permittivity `epsilon`. Find the value of a product `RG` for this system where `R` is the resistance of the medium between the conductors, and `C` is the mutual capacitance of the wires in the presence of the medium.

Two conductors of aribitary shape are embedded into an infinite homoge

1.	Two conductors of aribitary shape are embedded into an infinite homogenous poorly conducting medium with respectivity `rho` and permittivity `epsilon`. Find the value of a product `RG` for this system where `R` is the resistance of the medium between the conductors, and `C` is the mutual capacitance of the wires in the presence of the medium.
Answer» Let us mentally impart charges `+q` and `-q` to the conductors. As the mediuim is poorly conducting, the surfaces of the conductors are equipotential and the field configuration is same as in the absense of the medium. Let us surround for example the positively chagred conductor, by a closed surface `S`, just containing the conductor, then, `R = (varphi)/(i) = (varphi)/(int vec(j). d vec(S)) , (varphi)/(int sigma E_(n) dS), as vec(j) uarr uarr vec(E)` and `C = (q)/(varphi) = (epsilon epsilon_(0) int E_(n) dS)/(varphi)` So, `RC = (epsilon epsilon_(0))/(sigma) = rho epsilon epsilon_(0)`

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