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BASIC EQUATIONS OF MACROSCOPIC ELECTRODYNAMICS 15

between monopoles are quantum by nature, and we shall not pursue this topic here. The reader
interested in more details should consult [8, 9].
1.4.4 Magnetic Sensors

Later with better understanding of magnetic fields, we will introduce in a similar manner such
sensors as a magnetic monopole Δ , magnetic dipole moment , and volume density of

magnetic current

= ∆ [V ∙ s ∙ m]

� (1.8)
−2
= (∆ ⁄ ∆) [V ∙ m ]

Then
= ∯ ∘ [V]

� (1.9)
= ∫ [V ∙ s]

Here
= − ⁄ [V]

−3 � (1.10)
= lim (∆ ⁄ ∆) = ⁄ [V ∙ s ∙ m ]

∆→0
There are some problems with all these magnetic quantities. Wikipedia describes a magnetic
monopole as “…a hypothetical elementary particle in particle physics that is an isolated magnet
with only one magnetic pole.” It means the unseen presence of a north pole without a south
pole and vice versa. Such particles were predicted to exist by English physicist Paul Dirac in
1931 - and have never been seen in nature. Nonetheless, an international group of scientists in
the journal Nature reported on January 30 , 2014 about “…controlled creation of Dirac’s
th
monopoles in the synthetic magnetic field” at the temperature of few billionths of a degree
above absolute zero of −273.15°C. Eventually, it is currently difficult to talk about any practical
applications of this discovery.

A remarkable fact is that the magnetic current magnitude is measured in Volts (see 1.10)) and
thus physically equivalent to the voltage source like a battery. Consequently, it will be perfectly
valid without any mystics to interpret some sources of electromagnetic fields and field sensors
as magnetic charges, dipoles, and currents if the fields created by them and magnetic sources
are identical.
In fact, there is the critical obstacle to making such definitions because the magnetic monopole,
if it exists, must be an elementary particle similar to electron and proton, not a piece of material
with the magnetic current. Then one might wonder why we started this discussion at all. First
of all, we will show in the following sections that the introduction of magnetic charges and
currents makes Maxwell’s equations highly symmetrical. In physics as in most arts, the
symmetry is a sign of beauty, elegance, and validity. However, the practical reason is that some
man-made sources of electromagnetic fields act in the same way as magnetic charges and
currents. In other words, this abstract concept of magnetic charge and current substantially
simplifies the process of electromagnetic field solutions and significantly broadens their
diversity. That is why the “nonexistent” magnetic sources became the part of electromagnetics
almost from its birthday.