Question

Extra Credit: It is a fact that any three-dimensional vector field F can be expressed as a sum of vector fields F- G+H where G is curl-free (i.e. V x G 0) and H is divergence-free (i.e. H O. G and H are respectively called the longitudinal and tranverse parts of F. This is known as the Helmholz decomposition. It is important in electromagnetic theory. At any point in space the longitudinal part of the electric field describes the part of the field due to charged particles while the tranverse part describes the part of the electric field due to electromagnetic radiation in the vicinity of the point. Try to find the Helmholz decomposition for the vector field

Answer 1

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