The magnetic field inside an ideal long solenoid with n turns per unit length carrying current I is

1. Apply Ampere's law along a rectangular loop with one side inside and one outside. 2. The field outside is negligible; field inside is uniform and parallel to the axis. 3. Closed integral ∮B·dl = B·L = μ₀ · (nL · I). 4. Therefore B = μ₀nI inside an ideal long solenoid. _Source: syllabus Physics Ch 4 "Moving Charges and Magnetism", §4.8.1_