Both conservative and solenoidal vector field

  1. 1. The problem statement, all variables and given/known data

    if a vecor A is both solenoidal and conservative; is it correct that

    A=-▼Φ

    that is

    A=- gradΦ

    Φ is a scalar function

    thanks
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,808
    Staff Emeritus
    Science Advisor

    If A is just a conservative vector field, then [itex]A= -\nabla \phi[/itex] for some scalar function [itex]\phi[/itex]. I'm not sure what requiring that it also be solenoidal adds.
     
  4. well i thouhgt if A is only conservative
    then

    [itex]A= \nabla \phi[/itex] (according to my text book)

    not

    [itex]A= -\nabla \phi[/itex]

    so what is right?:confused:
     
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