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I am asked to prove that the self inductance of the system is given by

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I used Ampere's Law to find the magnetic field between the strips:

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The magnetic field due to the second strip would be the same which would yield a value of |B| =

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What bugs me is the last step to calculate the inductance, for which I have used two methods(with different answers):

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Something tells me that the first method is incorrect and I need some conceptual clarity. I am not able to figure out my mistake. Please help.

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You just messed up the dimensions a bit and forgot to consider the magnetic field due to the bottom sheet as well. The area through which the magnetic field is passing through is $al$, not $bl$.

So, it's $2((muknot)(I)/2b)*al=LI$ which gives us the correct answer.

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