# Inductance of two parallel wires

I've been asked to calculate the inductance per unit length for two wires or radius $a$ separated by $2d$ where $2d>>a$.

Starting from $\int_{s} B.dS = LI$ Im not sure what surface to take?

For each wire the field at a distance r away is given by $\int_{l} B.dl = \mu_0 I$ and by superposition $B$ in the first integral is their sum. And so $$LI= \int_{s} B_1.dS + \int_{s} B_2.dS$$ where $B_1$ and $B_2$ are the contributions from the two wires.

• An alternative derivation link – Sergei Gorbikov Aug 1 '16 at 13:16