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.