Continuamentenasconoifatti 1 aconfusionedelleteorie 2 Carlo Dossi
Electromagnetism is withoutany doubt a fascinating area of physics,
engineering and mathematics. Since the early pioneeringworks ofAmpere,
Faraday, and Maxwell, the scienti?cliteratureon this subject has become
immense, and books devoted to almost all of its aspects have been
published in the meantime. However,
webelievethatthereisstillsomeplacefornew booksdealingwithel-
tromagnetism, particularly if they are focused on more speci?c models,
or try to mix different levels of analysis: rigorous mathematical
results, sound numerical appro- mation schemes, real-life examples from
physics and engineering. The complete mathematical description of
electromagnetic problems is provided by the celebrated Maxwell
equations, a system of partial differential equations - pressed interms
ofphysical quantitiesliketheelectric?eld, themagnetic?eld and the
currentdensity.Maxwell scontributiontotheformulationofthese
equationsisrelated to the introductionof a speci?c term, called
displacement current, that he proposed to add to the set of equations
generally assumed to hold at that time, in order to ensure the
conservation of the electric charge. The presence of the displacement
current permits to describe one of the most - portant phenomenon in
electromagnetism, namely, wave propagation; however, in many interesting
applications the propagation speed of the wave is very high with respect
to the ratio of some typical length and time scale of the considered
device, and therefore the dominant aspect becomes the diffusionof the
electromagnetic ?elds. When the focus is on diffusioninstead of
propagation, from the modelingpointof view this corresponds to
neglecting the time derivative of the electric induction (i.e.,
thedisplacement current introducedby Maxwell)or, alternatively,
neglectingthe time derivative of the magnetic induction."
