# Divergence of curl in spherical coordinates

1. Apr 27, 2014

### joshmccraney

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!!

2. Apr 27, 2014

### lurflurf

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

3. Apr 28, 2014

### pasmith

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.

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