Capacitance and Inductance of Thin Metal Ribbons

[ehrenfest]

Homework Statement

21. A certain transmission line is constructed from two thin metal “ribbons”, of width w, a very small distance w<<h apart. The current travels down one strip and back the other strip. In each case it spreads out uniformly over the surface of the ribbon.
a) Find the capacitance per unit length.
b) Find the inductance per unit length.

Homework Equations

The Attempt at a Solution

Part a) is easy. I do not understand what part b) is asking. I can find the B-field between the ribbons. But I don't understand how inductance makes sense here. Inductance is defined by $\Phi = LI$. The magnetic flux $\Phi$ is the B-field per unit area. But here we have a volume not an area between the ribbons. I am so confused.

 

[Mindscrape]

Right, there is a volume between the ribbons, but there are also areas. Flux is how much of the field travels through a certain area, so you need to pick which area makes sense. Just ask yourself what direction does the magnetic field point in, and should I look length wise or width wise?