linguistic:paraphrasing
Magnetic field in magnetic circuit

The magnetic field created by an electromagnet is proportional to both N and I, hence this product, NI, is given the name magnetomotive force. For an electromagnet with a single magnetic circuit, Ampere's Law reduces to:

This is a nonlinear equation, because μ varies with B. For an exact solution, the value of μ at the B value used must be obtained from the core material hysteresis curve. If B is unknown, the equation must be solved by numerical methods.

Moreover, if the magnetomotive force is well above saturation, so the core material is in saturation, the magnetic field will be approximately the saturation value B for the material, and would not vary much with changes in NI. For a closed magnetic circuit (no air gap) most core materials saturate at a magnetomotive force of roughly 800 ampere-turns per meter of flux path.

For most core materials, μ r ≈ 2000 – 6000 {\displaystyle \mu _{r}\approx 2000{\text{–}}6000\,}. So in equation (2) above, the second term dominates. Therefore, in magnetic circuits with an air gap, B depends strongly on the length of the air gap, and the length of the flux path in the core does not matter much. Given an air gap of 1mm, a magnetomotive force of about 796 Ampere-turns is required to produce a magnetic field of 1T.