A simple proof is given of the theorem that an arbitrary divergenceless vector field F can be represented in terms of two scalar fields (Debye potentials) ψ and χ according to F=Lψ+∇×Lχ, where L is the angular momentum operator. The questions of uniqueness and completeness of this representation are discussed, and the importance of the theorem in electromagnetic theory is emphasized.
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© 1978 American Association of Physics Teachers.
1978
American Association of Physics Teachers
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