Editing Magnetic core (section)

===Hysteresis losses===
{{main|Magnetic hysteresis}}
When the magnetic field through the core changes, the [[magnetization]] of the core material changes by expansion and contraction of the tiny [[magnetic domain]]s it is composed of, due to movement of the [[Domain wall (magnetism)|domain wall]]s.  This process causes losses, because the domain walls get "snagged" on defects in the crystal structure and then "snap" past them, dissipating energy as heat.  This is called [[hysteresis loss]].  It can be seen in the graph of the ''B'' field versus the ''H'' field for the material, which has the form of a closed loop. 
The net energy that flows into the inductor expressed in relationship to the B-H characteristic of the core is shown by the equation<ref name="Kluwer Academic Publishers">{{cite book|last1=Erickson|first1=Robert|last2=Maksimović|first2=Dragan|title=Fundamentals of Power Electronics, Second Edition|date=2001|publisher=Kluwer Academic Publishers|isbn=9780792372707|page=506}}</ref>
:<math>W=\int{\left(nA_c\frac{dB(t)}{t}\right)\left(\frac{H(t)l_m}{n}\right)dt}=(A_cl_m)\int{HdB}</math>
This equation shows that the amount of energy lost in the material in one cycle of the applied field is proportional to the area inside the [[hysteresis loop]].  Since the energy lost in each cycle is constant, hysteresis power losses increase proportionally with [[frequency]].<ref>{{cite book|last1=Dhogal|first1=P.S.|title=Basic Electrical Engineering, Volume 1|date=1986|publisher=Tata McGraw-Hill Education|isbn=9780074515860|page=128}}</ref> The final equation for the hysteresis power loss is<ref name="Kluwer Academic Publishers"/>
:<math>P_H=(f)(A_cl_m)\int{HdB}</math>