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Source and vortex fields

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 rangę 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 electromagneticfields.