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Poynting vector
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==Uniqueness of the Poynting vector== The Poynting vector occurs in Poynting's theorem only through its [[divergence]] {{nowrap|β β '''S'''}}, that is, it is only required that the [[surface integral]] of the Poynting vector around a closed surface describe the net flow of electromagnetic energy into or out of the enclosed volume. This means that adding a [[solenoidal vector field]] (one with zero divergence) to '''S''' will result in another field that satisfies this required property of a Poynting vector field according to Poynting's theorem. Since the [[vector calculus identities#Divergence of the curl|divergence of any curl is zero]], one can add the [[Curl (mathematics)|curl]] of any vector field to the Poynting vector and the resulting vector field '''S'''β² will still satisfy Poynting's theorem. However even though the Poynting vector was originally formulated only for the sake of Poynting's theorem in which only its divergence appears, it turns out that the above choice of its form ''is'' unique.<ref name="Jackson1998" />{{rp|pp=258β260,605β612}} The following section gives an example which illustrates why it is ''not'' acceptable to add an arbitrary solenoidal field to '''E''' Γ '''H'''.
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