Two long straight wires wtih equal cross-sectional radii `a` are located parallel to each other in air. The distanace between their axes equals `b`. Find the mutal capacitances `b gt gt a`.

Explanation

Let us suppose that linear charge density of the wires be `lambda` then, the potential difference, `varphi_(+) - varphi_(-) = varphi - (-varphi) = 2varphi`. The intensity of the electric field created by one of the wires at a distance `x` from its axis can be easily found with the help of the Gauss's theorem,
`E = (lambda)/(2pi epsilon_(0) x)`
Then, `varphi = int_(a)^(b-a) E dx = (lambda)/(2pi epsilon_(0)) In (b-a)/(a)`
Hence, capacitance per unit length,
`(lambda)/(varphi_(+) - varphi_(-)) = (2pi epsilon_(0))/(In b//a)`