Source and vortex fields - wykład

Source and vortex fi elds In our study of electric and magnetic fields we will be greatly aided by the concepts of
sources and vortices, originally developed, as the names suggest, in the study of fluid
dynamics. The concepts themselves will be explained in the next section, but we will
remark first that
• An ability to form in the mind electromagnetic field pictures appears to be an
essential skill required for mastering electromagnetic theory.
• The source and vortex concepts provide a basis for picturing the electromagnetic
field created in a wide range of situations.
• In a theorem first proved by Helmholtz, it may be shown that any vector field may
be uniquely decomposed as the sum of two vector fields, one of which is purely
source type, and one of which is purely vortex type.
• The sources and vortices of a field are described in a mathematical sense by derivatives
of the vector calculus known as the divergence and curl derivatives.
• Maxwell's equations (which are the fundamental laws of electrodynamics) are when
placed in differential form direct statements about the source and vortex properties
of electromagnetic fields.
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