# A question On the deviation of the magnetic field in a solenoid using ampere's law and why we chose a specific ampereian loop

When we derive the magnetic field in a solenoid using ampere's law, we usually consider an ampereian loop such that it's bisected by one side of the transverse section of the solenoid (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.

• I apologize if this is off-topic, very lengthy,or has been posted already.I would also request the moderators not to add the homework tag for two reasons a)It 's not HW, it's a genuine doubt. b) I've asked questions in the past, and they were closed soon after the homework tag was added , I would like to avoid that if this is a new question. Aug 17, 2022 at 17:37