Capacitance between two crossed wires

free_electron

1. The problem statement, all variables and given/known data

I have two wires (length L) which are separated by a distance d. They are also oriented perpendicularly (but I am curious about the orientation impact, part of the question). By simplification, I assume them to be cylinders of radius R (in actuality they are likely strips). I expect R ~ d <<L. I would like to find the capacitance of such a system, where the two wires act as the electrodes.


2. Relevant equations

Gauss law: E=Q/(e0*2*pi*r*L) (r>R) (Field around a wire, cylindrical geometry)

=> V = integral of E vs distance between wires (R->d): V=Q/(e0*2*pi*L) ln (d/R)

3. The attempt at a solution

C=Q/V = (e0*2*pi*L)/ln(d/R)

The question has several little parts:

a) assuming the cylindrical geometry is the above calculation correct?

b) going to a realistic rectangular strip geometry, is there an analytical solution or can it only be numerically computed on a workstation? Can this solution be found at some public site?

c) How does the orientation matter?