# Self-inductance of a given Setup

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

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

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

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

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.

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.