# both conservative and solenoidal vector field

by aruna1
Tags: conservative, field, solenoidal, vector
 P: 111 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
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,713 If A is just a conservative vector field, then $A= -\nabla \phi$ for some scalar function $\phi$. I'm not sure what requiring that it also be solenoidal adds.
P: 111
 Quote by HallsofIvy If A is just a conservative vector field, then $A= -\nabla \phi$ for some scalar function $\phi$. I'm not sure what requiring that it also be solenoidal adds.
well i thouhgt if A is only conservative
then

$A= \nabla \phi$ (according to my text book)

not

$A= -\nabla \phi$

so what is right?

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