What Is Magnetic Flux Density?

Magnetic flux density is a vector field quantity that describes the strength and direction of a magnetic field at any point in space, defined as the magnetic flux per unit area crossing a surface perpendicular to the field. It is the quantity that appears in the Lorentz force law, the expression that governs the force exerted on a moving electric charge in a magnetic field. The SI unit of magnetic flux density is the tesla (T), adopted by the General Conference on Weights and Measures in 1960 in honor of Nikola Tesla; one tesla equals one weber per square meter (1 T = 1 Wb/m²) and equals 10,000 gauss in the older CGS unit system. The NIST description of the tesla unit notes that the tesla subsumes several earlier units and provides the unifying SI reference for magnetic measurement across engineering and science.

Magnetic flux density is sometimes distinguished from magnetic field strength (H), expressed in amperes per meter, by the relation B = µH, where µ is the permeability of the medium. In free space, µ equals the permeability of vacuum (µ₀ ≈ 1.257 × 10⁻⁶ H/m); inside a ferromagnetic material, µ can be thousands of times larger and depends on the applied field.

Physical Basis and Governing Equations

Magnetic flux density appears explicitly in two of Maxwell's four equations. Gauss's law for magnetism states that the divergence of B everywhere equals zero, meaning magnetic field lines form closed loops with no sources or sinks, an assertion that no isolated magnetic monopole has ever been observed. Faraday's law of induction states that the EMF around a closed loop equals the negative time derivative of the magnetic flux through that loop, where flux is defined as the integral of B over the enclosed area. These relations establish B as the primary magnetic field variable from which all macroscopic electromagnetic behavior can be derived.

Units, Scales, and Reference Values

The tesla spans an enormous range of physical situations. Earth's surface geomagnetic field is approximately 25 to 65 microtesla (µT), depending on latitude and local geology. A refrigerator magnet produces a surface field of roughly 5 mT. Clinical MRI systems operate at 1.5 T or 3 T, while research instruments reach 20 T or more using resistive or superconducting solenoids. The NIST Magnetic Sensing and Metrology program maintains calibrated reference fields spanning 10 fT to 20 T, traceable to SI electrical standards, to support calibration of measurement instruments across this full range. Fields relevant to fusion energy research and pulsed power systems can briefly exceed 100 T in specialized laboratory facilities.

Flux Density in Materials

Inside a magnetic material, the flux density B depends on both the externally applied field H and the magnetization M of the material itself, through the relation B = µ₀(H + M). Soft ferromagnetic materials such as silicon steel and permalloy reach saturation flux densities of 1 T to 2 T, which sets the upper operating limit for transformer and motor cores. Hard magnetic materials, used for permanent magnets, are characterized by their remanent flux density (the value of B when H returns to zero) and their coercivity (the reverse field needed to bring B to zero). The ScienceDirect overview of magnetic flux density provides a survey of how these material parameters govern device performance in power electronics and electromechanical systems.

Applications

Magnetic flux density has applications in a wide range of disciplines, including:

• MRI scanner design, where field uniformity at 1.5 T to 3 T determines image quality
• Power transformer core design, optimized to operate below magnetic saturation
• Magnetoresistive and Hall effect sensors measuring position, speed, and current
• Permanent magnet motors, where remanent flux density governs torque density
• Geophysical and navigational instruments exploiting Earth's ambient field