  The devices coil and transformer are subjects of interest in numerous
schoolbooks, in introductory scientific textbooks of physics and engineering,
and in laboratory courses at universities. Many descriptions, however, draw a
somewhat distorted picture of the underlying physical mechanisms and provide
half-knowledge or even clear misconceptions that should not be left uncommented
and are therefore studied in detail:
  (1) Primary and secondary voltage at a transformer have a different sign.
  (2) Electromagnetic induction is the only mechanism of importance for coils
and transformers.
  (3) The terminal voltage at coils and transformers is compensated by the
so-called "induced voltage" (emf), which explains why Kirchhoff's voltage law
also applies to coils and transformers.
  (4) The cores of coils and transformers are used for their ability to store
energy. Energy is transported from the primary to the secondary coil within the
magnetic core.
  (5) The stray magnetic and electric fields are sencondary effects not having
a major effect on energy transport.
  (6) The higher the load current, the easier a transformer goes into
saturation.
  (7) The higher the number of turns at the primary coil, the larger the
magnetic flux in the core.
  (8) Transformers with cores having an air gap have a lower coupling factor,
because the stray inductivity increases.
  In the paper, the most important characteristics of coil and transformers are
derived directly from Maxwell's equation for idealised conditions, and
subsequently, the different misconceptions are discussed and corrected.
