Magnetic field strength (H), magnetic induction (B), magnetization (M), and magnetic polarization (J) are four fundamental concepts in magnetism; while interrelated, they are sometimes easily confused. Distinguishing clearly between these four concepts is crucial for professionals working in the magnetic materials industry. Today, we will provide a detailed explanation of their definitions and the relationships between them.
Magnetic Field Strength (H)
Strictly speaking, magnetic field strength (H) is a physical quantity that lacks inherent physical significance. When it was originally defined, scientists hypothesized the existence of "magnetic charges"; however, it was later discovered that such entities do not exist—rather, magnetism is simply another manifestation of electric current.
In the early 1820s, scientists made a series of revolutionary discoveries that laid the foundation for modern magnetic theory.
In July 1820, the Danish physicist Hans Christian Orsted discovered that an electric current flowing through a conductor exerts a force on a magnetic needle, causing it to deflect and align itself. (The Orsted Experiment—the magnetic effect of electric currents.)
In September—just one week after news of this discovery reached the French Academy of Sciences—André-Marie Ampère successfully demonstrated through experimentation that two parallel current-carrying wires will attract each other if their currents flow in the same direction; conversely, if their currents flow in opposite directions, they will repel each other.
In 1825, Ampère published Ampère's Law, a fundamental principle describing the relationship between electric currents and the direction of the magnetic field lines generated by those currents.
Through mechanical measurements, it was determined that at points equidistant from a long, straight current-carrying wire, a magnetic needle experiences the same "magnetic field" strength; at points at varying distances, the "magnetic field" strength varies inversely with the distance from the wire. Thus, by combining mechanical measurements with the magnitude of the electric current, the physical quantity known as magnetic field strength (H) was defined. Its standard unit is amperes per meter (A/m). In the Gaussian system of units, the unit for H is the Oersted (Oe), where 1 A/m = 4π × 10⁻³ Oe.
While there are various interpretations of magnetic field strength (H), it can be conceptually simplified and understood as an *external* magnetic field (analogous to electric field strength—for instance, the magnetic field H applied to an object by means of an electric current I). Magnetic Induction *B*
Magnetic field strength (*H*) refers solely to the magnetic field generated by an external current. However, for ferromagnetic materials situated within a magnetic field, the internal particles—in addition to being influenced by the external field *H*—also generate an *induced* magnetic field in response to that external influence. Magnetic induction (*B*) represents the *total* magnetic field "perceived" by a particle; it is the vector sum of the applied external field *H* and the induced magnetic field *M* present at that specific location.
In a vacuum, magnetic induction is directly proportional to the external magnetic field—specifically, *B* = μ₀H, where μ₀ represents the permeability of free space (vacuum permeability). Within the interior of a ferromagnetic material, the magnetic induction is given by *B* = μ₀(H + M). This signifies that the total magnetic field is equal to μ₀ multiplied by the sum of the "magnetic field generated by the current (*H*)" and the "magnetic field generated by the medium (*M*) after being magnetized by *H*." The SI unit for *B* is the Tesla (T); in the Gaussian system of units, the unit is the Gauss (Gs), with the conversion being 1 T = 10⁴ Gs.
Strictly speaking, magnetic induction (*B*) represents the true "magnetic field strength" of a magnetic body. However, due to historical convention—where *H* was already designated as "magnetic field strength"—it became necessary to assign a distinct name to *B*: "magnetic induction." Both *B* and *H* fundamentally describe aspects of "magnetic field strength"; yet, because they are defined and derived through different conceptual frameworks, they possess different units. (In the Gaussian system, the unit for *B* is the Gauss [Gs], while the unit for *H* is the Oersted [Oe]; the conversion is 1 Oe = 1 × 10⁻⁴ Wb·m⁻² = 1 × 10⁻⁴ T = 1 Gs.)
Magnetic field strength (*H*) characterizes the magnetic field within a void or empty space; it disregards the presence of matter within that space, focusing instead on the relationship between the magnetic field and the current responsible for generating it. Conversely, magnetic induction (*B*) considers the ultimate strength of the magnetic field that results when actual matter is introduced into—and superimposed upon—that void-space field *H*; it focuses specifically on the actual magnetic field strength experienced within the material itself.
Magnetization (*M*)
As previously mentioned, magnetization (*M*) refers to the induced magnetic field generated by the internal particles of a material in response to an external magnetic field. Modern physics has demonstrated that every electron within an atom engages in two distinct forms of motion: orbital motion around the atomic nucleus and intrinsic spin motion. Both of these motions generate magnetic effects. If one views a molecule as a cohesive entity, the aggregate magnetic effect produced externally by all the electrons within that molecule can be represented by an equivalent circular current loop. This equivalent circular current is termed the *molecular current*, and its corresponding magnetic moment is called the *molecular magnetic moment*, denoted by pm. It represents the vector sum of the orbital magnetic moments and spin magnetic moments of all individual electrons within the molecule.
In the absence of an external magnetic field, the vector sum of all molecular magnetic moments within any arbitrary volume element inside a magnetic medium is zero. However, when the magnetic medium is placed within an external magnetic field, each molecule experiences a torque. This torque compels the molecular magnetic moments to align themselves in the direction of the external field. Consequently, under the influence of the external magnetic field, the vector sum of all molecular magnetic moments within any given volume element is no longer zero. Thus, the magnetic medium exhibits a certain degree of magnetism to the outside world—or, in other words, the magnetic medium has become *magnetized*. To characterize the magnetization state of the medium (specifically, its degree and direction of magnetization), we introduce the *magnetization vector* **M**, which represents the vector sum of all molecular magnetic moments per unit volume; its unit is A/m.
To investigate the relationship between this induced magnetic field **M** and the applied field **H**, we define the *magnetic susceptibility* as *χ* = M/H. A high magnetic susceptibility indicates that a given external magnetic field can generate a greater magnitude of internal induced magnetic field; conversely, a low magnetic susceptibility suggests that even a strong applied field elicits only a feeble response from the material—as if the material were "indifferent" to the external influence. Magnetic susceptibility can be either positive or negative. A positive susceptibility (*χ* > 0) signifies that the direction of the generated internal magnetic field **M** is aligned with that of the applied field **H**; a negative susceptibility (*χ* < 0) indicates that the additional magnetic field **M** induced within the material by **H** is directed opposite to the external field **H**.
**Magnetic Polarization J**
As discussed previously, the *magnetic induction* (or magnetic flux density) is given by *B* = μ0(H + M) = μ0H + μ0M. We define the term μ0M as the *magnetic polarization* of the material—that is, *J* = μ0M—and its unit is the Tesla (T). Physically, the magnetic polarization **J** is interpreted as the magnetic dipole moment per unit volume of the magnetic medium; it is also referred to as the *intrinsic magnetic induction*. It is typically denoted by the symbol Bi or J. In the Gaussian system of units, μ0= 1, and therefore **J** = **M**.
In soft magnetic materials, the magnetic field strength typically does not exceed 1000 A/m; given that μ₀ = 4 × 10⁻⁷ H/m and J = B – μ₀H, the difference between the magnetic induction B and the magnetic polarization J is therefore very slight. However, in hard magnetic materials, this distinction is highly significant; consequently, both the B = f(H) and J = f(H) characteristic curves are typically provided.
