Page 231 - Mechanics of Microelectromechanical Systems
P. 231
218 Chapter 4
The value of is not readily available in the literature because this
amount is rather a conceptual descriptor. A way of finding its value in terms
of other known amounts is briefly mentioned next. The magnetic dipole
moment m can be expressed as:
where is called magnetization, and for a linear and isotropic magnetic
material can be related to the magnetization field of the magnet as:
where is the magnetic permeability of the free space, and is the relative
permeability of the magnet, defined as the ratio of its permeability to the
permeability of the free space. The relative permeability of a given material,
other than air, is always larger than 1 and values are given for different
magnetic materials in the literature. By combining Eqs. (4.72), (4.76) and
(4.77) results in:
For anisotropic materials, the situation is a bit more complex because the
relative permeability cannot be represented by a single value. More details on
anisotropic magnetic material behavior can be found in Jakubovics [5] for
instance, and application of the anisotropic magnetic properties is explained
in more detail in Judy and Muller [6].
An attraction force ca be generated between a permanent magnet and a
ferroelectric layer (which can be magnetized), as a means of magnetic
transduction. Figure 4.37 is a sketch showing this principle.
Figure 4.37 Magnetic force between a permanent magnet and a ferroelectric substrate
The magnetic force can be calculated – see McCraig and Clegg [7] – as:
