# Both conservative and solenoidal vector field

1. Nov 12, 2008

### aruna1

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

Φ is a scalar function

thanks

2. Nov 12, 2008

### HallsofIvy

Staff Emeritus
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.

3. Nov 12, 2008

### aruna1

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?