Magnetic field strength H, magnetic flux density B, magnetization M, and magnetic polarization J are four very important fundamental concepts in magnetism. They are related but sometimes easily confused. Clarifying these four concepts is crucial for those working in the magnetic materials industry. Today, we will explain their concepts and relationships in detail.
Magnetic Field Strength H
Magnetic field strength H is actually a physical quantity without practical significance. Initially, it was defined based on the assumption of magnetic charge, but it was later discovered that this does not exist; it is simply the other side of electric current.
In the distant 1820s, scientists made a series of revolutionary discoveries that ushered in modern magnetic theory.
In July 1820, Danish physicist Hans Ørsted discovered that the current flowing through a conductor exerts a force on a magnetic needle, causing it to deflect. (Ørsted’s experiment—the magnetic effect of electric current)
In September, just one week after this news reached the French Academy of Sciences, Ampère successfully demonstrated through experiments that if the currents flowing in the same direction are attracted to each other, they will attract each other if they flow in opposite directions.
In 1825, Ampère published Ampère’s Law, a rule governing the relationship between the direction of the magnetic field lines of an electric current and the magnetic field it generates.
Through mechanical measurements, we can determine that at points equidistant from a long straight conductor, a compass needle experiences the same magnetic field strength; at points at different distances, the magnetic field strength is inversely proportional to the distance. Thus, we define the physical quantity of magnetic field strength H using mechanical measurements and current intensity. Its unit is ampere per meter (A/m). In the Gaussian unit system, the unit of H is Oe (1 A/m = 4π × 10⁻³ Oe).
There are many interpretations of magnetic field strength H. We can simplify it by understanding H as an external magnetic field (analogous to electric field strength; for example, using a current I to apply a magnetic field H to an object).
Magnetic induction intensity B
Magnetic field strength is merely the magnetic field generated by an applied current. For ferromagnetic materials within a magnetic field, in addition to the influence of the external magnetic field H, the particles within the material also generate an induced magnetic field under the influence of the external magnetic field. Magnetic induction intensity B represents the total magnetic field “senses” by a particle, which is the sum of the applied magnetic field H and the induced magnetic field M.
In a vacuum, magnetic induction intensity is directly proportional to the external magnetic field, i.e., B = μ0H, where μ0 is the permeability of free space. Inside a ferromagnetic material, the magnetic induction intensity B = μ0(H + M), meaning the total magnetic field equals μ0 multiplied by the sum of the magnetic field H generated by the current and the magnetic field M generated after the medium is magnetized by H. The unit of B is Tesla (T), which is Gaussian units (Gs), 1 T = 10 kgs.
Actually, magnetic induction intensity is the true “magnetic field strength” of a magnet, but because H has historically been referred to as magnetic field strength, B is given the alternative name of magnetic induction intensity. Both B and H refer to “magnetic field strength,” but their units differ due to different definitions and derivations (in the Gaussian system, B is in Gaussian units (Gs), while H is in Oersted units (Oe, 1 Oe = 1 × 10⁻⁴ Wb·m⁻² = 1 × 10⁻⁴ T = 1 Gs).
Magnetic field strength H is a magnetic field in a virtual space, disregarding matter within that space. It focuses on the relationship between the magnetic field and the current that generates it. Magnetic induction strength B, on the other hand, considers the strength of the final magnetic field after adding actual matter to the virtual magnetic field H. It focuses on the actual strength of the magnetic field generated by the matter.
Magnetization M
We have already mentioned magnetization M, which is the induced magnetic field generated by particles within matter under the influence of an external magnetic field. Modern physics has proven that each electron in an atom undergoes both orbital and spin motion around the nucleus, both of which produce magnetic effects. If we consider a molecule as a whole, the sum of the magnetic effects generated by all the electrons within the molecule can be represented by an equivalent circular current. This equivalent circular current is called the molecular current, and its corresponding magnetic moment is called the molecular magnetic moment, denoted by pm. It is the vector sum of the magnetic moments of all electron orbitals and the spin magnetic moments of the molecule.
In the absence of an external magnetic field, the vector sum of the magnetic moments of all molecules within any volume element of the magnetic medium is zero. However, when the magnetic medium is in an external magnetic field, each molecule experiences a torque that forces its magnetic moment to align with the direction of the external magnetic field. Therefore, under the influence of the external magnetic field, the vector sum of the magnetic moments of all molecules within any volume element is not zero. Thus, the magnetic medium exhibits a certain degree of magnetism, or in other words, it is magnetized. To describe the magnetization state (degree and direction of magnetization) of the magnetic medium, we introduce the magnetization vector M, which represents the vector sum of the magnetic moments of all molecules per unit volume, with units of A/m.
To study the relationship between this induced magnetic field M and the applied field H, we define the magnetic susceptibility χ = M/H. A high magnetic susceptibility means that the same external magnetic field can generate a greater internal induced magnetic field; a low magnetic susceptibility means that even with a large external magnetic field, the material inside will only respond weakly. Magnetic susceptibility can be positive or negative. A positive magnetic susceptibility χ > 0 indicates that the generated internal magnetic field M is in the same direction as the external magnetic field H. A negative magnetic susceptibility χ < 0 indicates that the additional magnetic field M generated inside the material due to H is in the opposite direction to the external field H.
Magnetic Polarization J
In the previous text, we introduced the magnetic induction intensity B = μ0(H + M) = μ0H + μ0M. We call μ0M the magnetic polarization intensity of the material, i.e., J = μ0M, and its unit is also T (Tesla). Magnetic polarization intensity J is physically interpreted as the magnetic dipole moment per unit volume of the magnetic medium, also called intrinsic magnetic induction intensity. Its symbol is Bi or J. In the Gaussian system, μ0 = 1, so J = M.
In soft magnetic materials, the magnetic field strength is usually no more than 1000 A/m, μ0 is 4×10-7H/m, and J=B-μ0H, so the difference between magnetic induction intensity B and magnetic polarization intensity J is very small; however, in hard magnetic materials, this difference is very significant, so usually two relationship curves, B=f(H) and J=f(H), are given.
