I have a vector field in Cartesian coordinates. I need to find its divergence, but I need the divergence to be in spherical coordinates. However, the divergence of this field is far easier to calculate in Cartesian coordinates.
Can I calculate the divergence of the vector field in Cartesian coordinates, and then substitute appropriate values to convert the divergence into spherical coordinates? Or do I have to convert the vector field into spherical coordinates first, and then calculate the divergence?
Trying both of these methods yielded different (but somewhat similar) results - but this may simply be due to algebraic errors in my conversion, and not errors in the concept itself.