[Uni Physics 2] Inductance Problem

[jonathanlv7]

Homework Statement

Two identical long wires of radius a = 2.90 mm are parallel and carry identical currents of i = 5.00 A in opposite directions. Their center-to-center separation is W = 17.0 cm. Neglect the flux within the wires but consider the flux in the region between the wires. What is the inductance per unit length of the wires?

The problem looks like this | |

Homework Equations

L = Flux/Current Flux = B*A

The Attempt at a Solution

What I did was integrate (10^-7)2I/x from r to w-r. After the integration I multiplied by d (variable I assigned as the height of the configuration) because I need the total magnetic field that goes through the entire area between the wires.

Then I doubled this result because both wires create magnetic fields with the same magnitude and direction in the entire area. Next, I multiplied this result by the area of the section between them which I got to be d(w-2r) -- d is the height of the wires, however, I am aware that in the context of the problem the wires are infinitely long. Lastly I divided by I*d to get the inductance. My final expression is 4d(w-2r)(10^-7)[ln(w-r)-ln(r)] I calculated the answer and it is wrong. Some help would be amazing! Thanks!
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[gleem]

First your notation for inductance is incorrect.

L =Φ/I

Your approach is correct but You do not need to know or assume the "height" of the array. Since you want the inductance/ length you just need to find the flux . per unit length (dΦ) , i.e. the incremental inductance/length =( incremental flux/length) /current

dL = dΦ/I =∫ ( B_a+B_b )⋅da/I = 2⋅∫B.dl.dx/I where x is the distance from the wire.

∴ dL = 2⋅ dl⋅∫B⋅dx/I --> dL/dl = 2⋅∫B⋅dx/I where the integral is taken from r to, not w-r but, ?