Editing Electromagnet (section)

==== Magnetic field in magnetic circuit ====
The magnetic field created by an electromagnet is proportional to both the number of turns of wire <math>N</math> and the current <math>I</math>; their product, <math>NI</math>, is called [[magnetomotive force]]. For an electromagnet with a single [[magnetic circuit]], Ampere's Law reduces to:<ref name="Merzouki" /><ref>{{cite book
  | last = Feynman
  | first = Richard P.
  | title = Lectures on Physics, Vol. 2
  | publisher = Addison-Wesley
  | year = 1963
  | location = New York
  | pages = 36–9 to 36–11, eq. 36–26
  | isbn =  978-8185015842
  | url = https://www.feynmanlectures.caltech.edu/II_36.html#Ch36-S5
}}</ref><ref name="Fitzgerald">{{cite book
  | last1 = Fitzgerald
  | first1 = A.
  | last2 = Kingsley |first2=Charles |last3=Kusko |first3=Alexander
  | title = Electric Machinery, 3rd Ed
  | publisher = McGraw-Hill
  | year = 1971
  | location = USA
  | pages = 3–5}}</ref>

:<math>NI = H_{\mathrm{core}} L_{\mathrm{core}} + H_{\mathrm{gap}} L_{\mathrm{gap}}</math>
{{NumBlk|:|<math>NI = B \left(\frac{L_{\mathrm{core}}}{\mu} + \frac{L_{\mathrm{gap}}}{\mu_0} \right) </math>|{{EquationRef|3}}}}

This is a [[nonlinear equation]], because the permeability of the core <math>\mu</math> varies with <math>B</math>. For an exact solution, <math>\mu(B)</math> must be obtained from the core material [[Hysteresis loop|hysteresis curve]].<ref name="Merzouki" /> If <math>B</math> is unknown, the equation must be solved by [[Numerical analysis|numerical methods]].  

However, if the magnetomotive force is well above saturation (so the core material is in saturation), the magnetic field will be approximately the material's saturation value <math>B_{sat}</math>, and will not vary much with changes in <math>NI</math>. For a closed magnetic circuit (no air gap), most core materials saturate at a magnetomotive force of roughly 800&nbsp;ampere-turns per meter of flux path.

For most core materials, the relative permeability <math>\mu_r \approx 2000 \text{–} 6000\,</math>.<ref name="Fitzgerald" /> So in ({{EquationNote|3|Eq. 3}}), the second term dominates. Therefore, in magnetic circuits with an air gap, <math>B</math> 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&nbsp;ampere-turns is required to produce a magnetic field of 1&nbsp;T.