# Divergence of curl in spherical coordinates

• member 428835

#### member 428835

Hey pf!

I was thinking about how div(curl(f)) = 0 for any vector field f. However, is this true for div and curl in spherical coordinates? It doesn't seem to be.

If not, what needs to happen for this to be true in spherical coordinates??

Thanks all!

div and curl do not depend on coordinates so the result holds for all coordinates including spherical

Keep in mind you omitted some conditions, f must be well behaved for that to be true

Hey pf!

I was thinking about how div(curl(f)) = 0 for any vector field f. However, is this true for div and curl in spherical coordinates? It doesn't seem to be.

If not, what needs to happen for this to be true in spherical coordinates??

Thanks all!

If you don't get $\nabla \cdot (\nabla \times F) = 0$ for well-behaved $F$ in spherical coordinates then you are making an error in your calculations, such as forgetting that the basis vectors are functions of position and not constant as in the Cartesian case.