. how can vector field be expressed as the gradient of scalar filed?
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How do you prove that a vector field E that is irrotational (∇×E=0) may be written as −∇ϕ for a scalar field ϕ? I have been trying to use the identity about the expansion of ∇(A⋅B) but can't thing of a suitable second vector field. I'm sure I remember it being something like ϕA for some scalar field ϕ and fixed vector A. I have also tried having the second vector as ∇A but that doesn't seem to work either. Maybe it must be some function of E?
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