H-field
An auxiliary vector field that describes the driving magnetic influence produced by free currents, independent of the material's response.
H-field: magnetic force divorced from material response
The H-field is a vector field that describes the magnetic driving force produced by electric currents alone, stripped of any influence from the material in which those currents flow. In SI units it is measured in amperes per meter (A/m). It answers the question: what magnetic influence would exist if we ignored how the material itself magnetically responds? The companion quantity, the B-field (magnetic flux density), tells you the complete magnetic result after the material has responded, including its permeability.
In free space, H and B are related by a simple constant: B equals mu-zero times H, where mu-zero is the permeability of free space (approximately 1.257 × 10−6 henry per meter). Inside a material with permeability mu, the relationship becomes B equals mu times H. This distinction matters because different ferromagnetic materials, different alloys, different temperatures, and different magnetic histories will produce different B-fields from the same H-field. H is the input; B is what you actually measure or care about in practice.
Where H-field appears in real work
In transformer design, coil winding, and magnetic circuit analysis, engineers specify H-field to avoid confusion between the magnetizing force (which depends only on current and geometry) and the resulting flux density (which also depends on core material and saturation). In ferromagnetic materials used in rotating machinery, permanent magnets, or magnetic shielding, the H-field tells you how hard you are pushing magnetically; the B-field tells you how the material pushes back. This separation becomes critical when materials saturate, lose their permeability, or exhibit hysteresis.
The term originates from historical convention in electromagnetics, where H was introduced to handle the complexity of magnetization in materials. The name itself is sometimes attributed to the German physicist Hermann von Helmholtz, though the letter choice has become arbitrary. In older texts and non-SI systems, H-field may be expressed in oersteds or different unit schemes, but A/m is standard in modern engineering.
Confusion between H and B is common among newcomers because both describe magnetism, but they answer different questions. H is what you apply; B is what you get. In vacuum or air, this distinction is trivial. In iron, nickel, or specialized magnetic alloys, it is everything.