(like in the picture above)
I also understand from Question on Ampere's Law and Solenoid that we don't draw a loop that encloses the entire solenoid as ampere's law doesn't give us the magnetic field, but the line integral of the dot product of B and l.
however, I'm unable to understand why we don't consider two loops(each one enclosing the current on each side).such that these loops intersect at the center of the loop . I do understand that ampere's law is a line integral and the sum of the line integrals(when we add up the contributions of both loops is zero). however, I'm unable to understand why if the line integral each loop , taken individually gives us the magnetic field, why doesn't the sum of both loops give us the same?
Moreover, leaving ampere's law aside, as we're only considering half the current passing via the solenoid, shouldn't the field be 2μnI
where μ is the permeability of free space, n is the number of turns per unit length and I is the current passing through the circuit.