What Is Magnetic Flux Density?

Magnetic flux density is a vector field quantity, designated B, that describes the strength and direction of a magnetic field at a point in space. Its SI unit is the tesla (T), where one tesla equals one weber per square meter (Wb/m²). Unlike magnetic flux, which is a scalar total over a surface, flux density is a local, directional quantity: it specifies how intensely and in what direction the field acts at every individual point. Flux density is the quantity that appears directly in the Lorentz force law and in the constitutive relations linking field intensity to material response.

Magnetic flux density is distinct from magnetic field intensity H, which is measured in amperes per meter. The two are related through the permeability of the medium: B = μH, where μ = μ₀μᵣ, the product of the permeability of free space (4π × 10⁻⁷ H/m) and the relative permeability of the material. In vacuum and nonmagnetic materials μᵣ ≈ 1, but in ferromagnetic materials it can reach tens of thousands, and the relationship becomes nonlinear.

The B-H Curve and Magnetic Hysteresis

The relationship between B and H in ferromagnetic materials is captured by the magnetization curve, commonly called the B-H curve or hysteresis loop. Starting from an unmagnetized state, increasing H drives B upward along the initial magnetization curve until the material saturates, at which point additional field produces diminishing returns. When H is then reduced, B does not retrace the same path but lags behind, a phenomenon called hysteresis. The Electronics Tutorials treatment of magnetic hysteresis explains how the area enclosed by the hysteresis loop is proportional to the energy dissipated as heat per magnetization cycle. Two quantities read from the loop are critical in material selection: the remanence Bᵣ, the flux density retained when H returns to zero, and the coercive field Hc, the reverse field needed to reduce B to zero. Soft magnetic materials have narrow loops with low coercivity; hard magnetic materials have wide loops with high coercivity and high remanence, making them suitable for permanent magnets.

Measurement Techniques

Measuring magnetic flux density accurately requires instruments calibrated to the tesla or its subunits. Hall effect sensors are the most widely deployed measurement devices: a current-carrying semiconductor slab placed perpendicular to B develops a transverse voltage, the Hall voltage, proportional to the local flux density. Texas Instruments' application note on Hall effect sensor data sheets details how sensitivity, offset, and temperature coefficients must be characterized to achieve measurement uncertainties below one percent. For precision laboratory measurements, teslameters using three-axis Hall probes achieve uncertainties on the order of 0.01%, as described in IEEE Transactions on Instrumentation and Measurement work on integrated Hall probe teslameters. Fluxgate magnetometers and superconducting quantum interference devices (SQUIDs) extend measurable range down to femtotesla levels for geophysical and biomedical applications.

Magnetic Moments and Flux Density in Materials

At the atomic scale, magnetic flux density in a material reflects the collective alignment of magnetic moments carried by electrons. In ferromagnetic materials such as iron, nickel, and cobalt, exchange interactions cause moments in neighboring atoms to align parallel, producing a spontaneous magnetization and a correspondingly large B even without an external field. Antiferromagnetic materials have antiparallel moment arrangements that cancel, yielding zero net magnetization but a structured internal field pattern. The macroscopic flux density in a material equals μ₀(H + M), where M is the magnetization per unit volume, so measuring B and knowing H allows M to be derived and used to characterize material properties.

Applications

Magnetic flux density has applications across a wide range of engineering and scientific areas, including:

• Electric motor and transformer design, where core saturation limits and B-H characteristics govern efficiency and size
• Medical MRI scanners, which operate at static flux densities of 1.5 T, 3 T, or 7 T to achieve adequate signal-to-noise ratio
• Hall effect current sensors in power electronics, where B proportional to conductor current is measured without galvanic contact
• Magnetic particle inspection, where controlled flux density is used to reveal surface-breaking defects in steel components
• Superconducting magnet characterization, where field mapping across the bore verifies homogeneity specifications