Magnetostatic solutions: permanent magnets

As the final topic in two-dimensional magnetostatics, we’ll consider solutions with permanent magnets. To start, it’s useful to review how permanent magnets work. Introductory electromagnetic texts often don’t treat the topic, and the explanations in many specialized references are overly complex.

The electrons of many atoms carry a circulating current, like a small current loop. Such an [...]

Magnetostatic solutions: when steel gets complicated

Material properties are the reason why magnetostatic solutions are generally more involved than electrostatic solutions. Dielectrics can usually be characterized by a single value of relative dielectric constant εr up to the point where they break down. On the other hand, magnetic materials do interesting things even at normal values of flux density B:

Magnet steels may exhibit [...]

Test magnetostatic solution: the role of steel in magnet design

To complete our study of the solenoid coil, we’ll proceed to a practical design by adding a magnet-steel shield. Here, the term magnet-steel designates a soft material with high relative permeability. The term soft means that the steel has a narrow hysteresis curve and with little permanent magnetization. In this article, we’ll concentrate on numerical methods [...]

Test magnetostatic solution: boundary effects and automatic operation

The previous article emphasized that finite-element calculations are performed in a finite volume and that conditions on the the boundaries must be specified. We use a Neumann condition (field lines normal to the boundary) along a symmetry plane. An example is one half of a magnetic mirror split at the midplane. Otherwise, the most common boundary [...]

Test magnetostatic solution: simple coil with boundaries

In this article, we’ll advance to 2D magnetostatic solutions using the programs Mesh and PerMag. The previous articles on electrostatics have given background on the basic concepts of FEM calculations and program operation. Therefore, in this lecture and following ones I’ll concentrate on the special features of magnetic field calculations. In preparation, I suggest you try [...]