Question

Two long straight wires with equal cross-sectional radii $a$ are located parallel to each other in air. The distance between their axes equals $b$. Find the mutual capacitance of the wires per unit length under the condition $b >> a$.

Answer 1

$\frac{\pi \epsilon_0}{\ln(b/a)}$

Answer 2

The capacitance per unit length of two parallel wires is $C/L = \frac{\pi \epsilon_0}{\cosh^{-1}(b/2a)}$. For $b >> a$, $\cosh^{-1}(b/2a) \approx \ln(b/a)$. Thus, $C/L \approx \frac{\pi \epsilon_0}{\ln(b/a)}$.