Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 148

If a magnetic material is placed in an applied magnetic field of strength H, the individual atomic magnetic moments contribute to its overall response such that the internal field strength B in the material, also called the magnetic induction or magnetic flux density, is given by

(4.40)

where, μ_o is a physical constant called the permeability of free space (equal to 1.257 × 10⁻⁶ H/m) and M is the magnetic moment per unit volume of the material, commonly referred to as its magnetization. B, H, and M are vectors but to simplify the discussion, we will not emphasize this point and just consider their magnitude. As the magnetic flux density in a vacuum B_o is equal to μ_o H, the term μ_o M represents the change in the flux density due to the presence of the material.

A few different parameters are used to classify the magnetic properties of magnetic materials. The magnetic susceptibility χ_m, defined by

(4.41)

relates the magnetization induced in a material by an applied field H. As both M and H have the same units (A m), χ_m is unitless, that is, a number without units. The relative permeability μ_r is defined as

(4.42)

where, μ is the permeability of the material. The susceptibility or the relative permeability provides a measure of the degree to which a material can be magnetized by an applied field. They are related by

(4.43)