Magnetic field created by a current
The magnetic field created by an electromagnet is proportional to both the number of turns in the winding, N, and the current in the wire, I, hence this product, NI, in ampere The ampere is the SI unit of electric current. The ampere, in practice often shortened to amp, is an SI base unit, and is named after André-Marie Ampère, one of the main discoverers of electromagnetism-turns, is given the name magnetomotive force Magnetomotive force (SI Unit: At) is any physical force that produces magnetic flux. In this context, the word "force" is used in a general sense of "work potential", and is analogous to, but distinct from mechanical force measured in newtons. Therefore it is analogous to electromotive force i.e. voltage. For an electromagnet with a single magnetic circuit The concept of a 'magnetic circuit' exploits a one to one correspondence between the equations of the magnetic field in a non-hysteretic material to that of an electrical circuit. Using this concept the magnetic fields of complex devices such as transformers can be quickly solved using the methods and techniques developed for electrical circuits, of which length Lcore is in the core material and length Lgap is in air gaps, Ampere's Law reduces to:[10][11]
-
- where
- is the permeability of free space (or air).
This is a nonlinear equation In mathematics, a nonlinear system is a system which is not linear, that is, a system which does not satisfy the superposition principle, or whose output is not proportional to its input. Less technically, a nonlinear system is any problem where the variable to be solved for cannot be written as a linear combination of independent components. A, because the permeability of the core, μ, is a function of the magnetic field. For an exact solution, the value of μ at the B value used must be obtained from the core material hysteresis curve A system with hysteresis has memory. This means that the system may be in more than one state, and that the system's current state is independent of its input at the current instant in time. A system with hysteresis is said to exhibit path-dependence, or "rate-independent memory".. If B is unknown, the equation must be solved by numerical methods Numerical analysis is the study of algorithms for the problems of continuous mathematics. However, if the magnetomotive force is well above saturation, so the core material is in saturation, the magnetic field won't vary much with changes in NI anyway. 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, .[11] So in equation (1) above, the second term dominates. Therefore, in magnetic circuits with an air gap, the behavior of the magnet depends strongly on the length of the air gap, and the length of the flux path in the core doesn't matter much.
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