Since the wires are infinite, so the system of these two wires can be considered as a closed rectangle of infinite length and breadth equal to d. flux through the strip:
ϕ=∫d−aaμ0I2πr(ldr)=μ0Il2πIn(d−aa)ϕ=∫ad-aμ0I2πr(ldr)=μ0Il2πIn(d-aa)The other wire produces the same result, so the total flux through the dotted rectangle is
ϕ→tal=μ0lIπIn(d−aa)ϕ→tal=μ0lIπIn(d-aa)
The total inducatance of lengthll
L=ϕ→talI=μ0lπIn(d−aa)L=ϕ→talI=μ0lπIn(d-aa)
Inductance per unit length=Ll=μ0πIn(d−aa)