Divergence and curl

1. Aug 26, 2007

ehrenfest

I am trying to think of a non-constant function whose divergence and curl is 0. It seems like this is impossible to me. Any hints?

2. Aug 26, 2007

siddharth

Well, if the curl is zero, you can write the field as a gradient of some scalar function. So, if the divergence is also zero, what does that tell you? (Hint: Laplace equation)

3. Aug 26, 2007

arildno

Potential theory would be dreadfully boring to study if the Laplace equation had only constant solutions..