In recent years, more courses in electromagnetism are using the “Système International” (SI) units as opposed to Gaussian-cgs. The confusing notation used to formulate SI with origins in the early 19th century still persists in instruction. This work shows that electromagnetism may be taught relatively painlessly in the units that virtually everyone uses by employing a new presentation that makes the equations nearly as simple as those in the Heaviside–Lorentz system commonly used by theoretical physicists. Introducing a new coupling constant κ and some new notation for the fields, it is possible to dispense with ϵ0 and μ0 and the conceptual framework from which they come. As a result, it is possible achieve much greater clarity, while using all the same symbols and relations as in the extant literature.
References
1.
See, for example,
George
Trigg
, “Dimensions and units in electromagnetism
,” Am. J. Phys.
15
, 117
(1957
);Dwight W.
Berreman
, “Electromagnetic equations in generalized units
,” Am. J. Phys.
27
, 515
–516
(1959
);Dwight W.
Berreman
, “Electromagnetic equations written in a form independent of the system of units
,” Am. J. Phys.
27
, 44
–46
(1959
).2.
This argument is less persuasive if one regards the electrostatic force as an action at a distance.
3.
One might ask whether there could be a separate κ for the creation and the response to the field. This would be forbidden by CPT symmetry and, thus, by quantum field theories.
4.
Our familiar sphere, which embeds in three dimensions, is called a two-sphere. Interestingly, there is one additional π at each odd dimension.
5.
One can measure fields without defining a unit of charge using the u result. Place a positive charge on a plate of a parallel-plate capacitor and an equal negative charge on the other. Connect the plates via a resistive wire. Without reference to the charges, one knows that the heat Q generated in the resistor during discharge is the energy originally contained in the electrostatic field between the plates. If the separation of the plates is small compared to the other dimensions, the electric field is uniform between the plates and nearly zero outside. Thus, , where v is the volume of the capacitor.
6.
Technically, unless we change the Lorentz force law convention for , setting actually yields the obsolete ESU system.
7.
For a history of electromagnetic units, see, for example,
Neal
Zimmerman
, “A primer on electrical units in the Système International
,” Am. J. Phys.
66
, 324
–331
(1998
);Francis B.
Silsbee
, “Systems of electrical units
,” J. Res. Natl. But. Stand. C
66
(2
), 137
–178
(1962
).8.
By definition, , and . The best current value for is ; see <https://physics.nist.gov/cuu/Constants>.
9.
This distinction is usually hidden in the Gcgs and HL units, because charge is treated as a derived unit. However, one can keep track of dimensions by measuring charge in U even in Gcgs and HL systems, by using the relation .
10.
For the early history of the meaning of these entities, see
Jeb
Buchwald
, From Maxwell to Microphysics, Aspects of Electromagnetic Theory in the Last Quarter of the Nineteenth Century
(University of Chicago
, Chicago
, 1985
), Chap. 3;11.
Note that e in the different systems differs only by the choice of length and mass units, and b differs in addition by the factor of c.
12.
This analysis also reveals that P and M can be considered as having different units from D and H in the Gcgs and HL systems, since the latter are conventional fields measured with U in the denominator and the former are sources measured with U in the numerator, cf.
J. D.
Jackson
, Classical Electromagnetics
, 3rd ed. (John Wiley & Sons
, New York
, 1999
), p. 780
.13.
Since measurements of the magnetic field H are sometimes seen, H still has to be introduced to students. One plus is that , a quantity that is often encountered.
© 2022 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2022
Author(s)
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