# Encyclopedia Magnetica

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# Confusion between B and H

 Stan Zurek, Confusion between B and H, Encyclopedia Magnetica, E-Magnetica.pl

Confusion between B and H - a problem recognised in the literature regarding magnetic field and the confusion between the quantities, meaning and physical units of magnetic flux density B and magnetic field strength H.1)2)3)4)5)

From engineering viewpoint, in ferromagnets flux density B is a different physical quantity from magnetic field strength H: $$B \neq H$$

Both B and H are strictly defined in terms of measurement units as well as their physical meaning.6)2) Only the names are problematic, not the units or mathematical calculations.7)

The confusion arises because different authors have various scientific background, so different emphasis is put on different aspects of the analysis, calculation, and experimental approach.

Richard Feynman, The Feynman Lectures on Physics:1)
Most people who use the mks units have chosen to use a different definition of H. Calling their field H′ (of course, they still call it H without the prime) […]
We think it is more convenient for H to have the same units as B — rather than the units of M, as H′ does. […] There is one more horrible thing. Many people who use our definition of H have decided to call the units of H and B by different names! […] So, in many books you will find graphs with B plotted in gauss and H in oersteds. They are really the same unit — 10−4 of the mks unit. We have summarized the confusion about magnetic units in […]

Two broad approaches can be identified:

1. In theoretical physics - magnetic field B is regarded as “fundamental”, and H is “useful” but “has no name”8)7)9) Matter is treated at both the microscopic level (B in the vacuum between the atoms) as well as macroscopic (M, H).

2. In engineering - the “fundamental” magnetic field is H;10) electric current I generates the magnetic field strength H, and flux density B is a response of the medium magnetised by H. The engineering approach follows the naming convention defined in the SI system of units.6) All the quantities are measurable at the macroscopic level.

There are also two more quantities, closely related to H and B: magnetisation M (measured in A/m) and magnetic polarisation J (measured in T).11)12)13)

### Generation of H

Electric current I generates magnetic field, in the form of magnetic field strength H, regardless the type of the surrounding medium

Electric current I produces around itself magnetic field strength H, whose amplitude is independent of the type of a continuous isotropic medium (regardless if it is non-magnetic, magnetic, non-linear, etc.)2)

For an infinitely long straight round wire it is:

 (4) $$H = \frac{I}{2 ⋅ \pi ⋅ r}$$ (A/m)

where: r - radius of a circle enclosing the current I, π - the mathematical constant.

For other geometries of conductors (current loop, solenoid, etc.) the value of H can be calculated from the Ampere's circuital law.47)11)

## References

6), 6), 6), 6)
14) IEEE Magnetics, MAGNETIC UNITS, {accessed 2021-05-01}
25) Charles Proteus Steinmetz, On the law of hysteresis, The Electrician, A weekly illustrated Journal of Electrical Engineering, Industry and Science, Vol. XXVIII, November 6 1891 to April 29, 1892
32) ASTM standard A343/A343M − 14, Standard Test Method for Alternating-Current Magnetic Properties of Materials at Power Frequencies Using Wattmeter-Ammeter-Voltmeter Method and 25-cm Epstein Test Frame, 2014
36) J.A. Ewing, Magnetic induction in iron and other metals, 2nd issue, The D. Van Nostrand Company, New York, 1894
45) S. N. Ghosh, Electromagnetic Theory and Wave Propagation, CRC Press, 2002, ISBN 9780849324307, p. 51
49) There was no separate entry titled “magnetic field strength” at the time of writing this article {accessed 2020-03-07}. The brief definition was included in the entry Magnetic field, Encyclopædia Britannica Online, {accessed 2020-03-07}.
50) There was no separate entry titled “magnetic flux density” at the time of writing this article {accessed 2020-03-07}. The brief definition was included in the entry Magnetic field, Encyclopædia Britannica Online, {accessed 2020-03-07}.