Aspects of this topic are discussed in the following places at Britannica.
...H, caused by the current forces some or all of the atomic magnets in the material to align with the field. The net effect of this alignment is to increase the total magnetic field, or magnetic flux density B. The aligning process does not occur simultaneously or in step with the magnetizing field but lags behind it.
Magnetic fields may be represented mathematically by quantities called vectors that have direction as well as magnitude. Two different vectors are in use to represent a magnetic field: one called magnetic flux density, or magnetic induction, is symbolized by B; the other, called the magnetic field strength, or magnetic field intensity, is symbolized by H. The magnetic field...
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