Both conservative and solenoidal vector field

[aruna1]

Homework Statement

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

 

[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.

 

[aruna1]

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 textbook)

not

$A= -\nabla \phi$

so what is right?