Manipal Entrance Test 2015 Physics Paper

Since, the wires are infinite, so the system of these two wires can be considered as closed rectangle of infinite length and breadth equal to d.
Flux through strip
ϕ=

d−a

∫

a

µ0I

2πr

(l‌dr) =

µ0‌Il

2π

‌ln(

d−a

a

)
The other wire produces the same result, so the total flux through the rectangle ABCD is
ϕtotal=

µ0‌Il

π

‌ln(

d−a

a

)
The total inductance of length l
L=

ltotal

I

=

µ0I

π

‌ln(

d−a

a

)
Inductance per unit length =

L

l

=

µ0

π

‌ln(

d−a

a

)