Magnetic Flux Density, Magnetic Field Strength, and the Permeability of Vacuum

The International System of Units (SI) will be revised on 20 May 2019 such that all seven base units, including the kilogram, will be defined in terms of fixed numerical values of seven defining constants. The revised SI will include a redefinition of the ampere. One consequence is that the permeability of vacuum μ₀, equal to the ratio of magnetic flux density B to magnetic field strength H, will not have a fixed numerical value of 4π × 10⁻⁷ N/A², but will become a measurable quantity. This prompts a review of historical arguments on the concepts of B and H, whether they are conceptually identical in vacuum, and whether their nature depends on the system of units used to express them. The argument can be made that, in vacuum, B is physically the same as H in all systems of units, but in the revised SI, it is helpful to recognize B as the primary magnetic field vector, μ₀ as an experimental constant, and H as an arithmetically derived auxiliary vector. This does not affect the traditional Maxwellian definition of magnetic susceptibility, equal to M/H (not M/B), nor detract from the utility of M−H and B−H curves to characterize magnetic materials.

R. B. Goldfarb, “The permeability of vacuum and the revised International System of Units” (editorial), IEEE Magn. Lett. 8, 1110003 (2017), doi: 10.1109/LMAG.2017.2777782.

R. B. Goldfarb, “Electromagnetic units, the Giorgi system, and the revised International System of Units,” IEEE Magn. Lett. 9, 1205905 (2018), doi: 10.1109/LMAG.2018.2868654.