Current Sources
If all currents in a system are known (i.e., if a complete description of is available) then the magnetic field can be determined from the currents by the Biot-Savart equation:
This technique works well for problems where the medium is a vacuum or air or some similar material with a relative permeability of 1. This includes Air core inductors and Air core transformers. One advantage of this technique is that a complex coil geometry can be integrated in sections, or for a very difficult geometry numerical integration may be used. Since this equation is primarily used to solve linear problems, the complete answer will be a sum of the integral of each component section.
For problems where the dominant magnetic material is a highly permeable magnetic core with relatively small air gaps, a magnetic circuit approach is useful. When the air gaps are large in comparison to the magnetic circuit length, fringing becomes significant and usually requires a finite element calculation. The finite element calculation uses a modified form of the magnetostatic equations above in order to calculate magnetic potential. The value of can be found from the magnetic potential.
The magnetic field can be derived from the vector potential. Since the divergence of the magnetic flux density is always zero,
and the relation of the vector potential to current is:
where is the current density.
Read more about this topic: Magnetostatics, Solving For The Magnetic Field
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