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(This question may be more appropriate for Math Stack Exchange, but since physicists tend to be more well acquainted with vector calculus, I'm asking the question here).

This question is about convective operators. Please open the Wolfram MathWorld page (accessed March 08, 2014).

Lets assume that the vector field ${\bf{B}}(x)$ is constant in all space. Then according to equation (2) (which is the formula in Cartesian coordinates) the result of the operator is the zero vector field, since ${\bf{B}}$ appears only in derivatives.

But in equation (4) (spherical coordinates) there are also terms where ${\bf{B}}$ is not in a derivative, and so the results could be different from zero.

How is this possible?

(By the way, the same formula appears in Wikipedia (accessed March 08, 2014))

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First, please answer this simple question: How to write a constant (in all space) vector in spherical coordinates?

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  • $\begingroup$ Ok, I get it. Stupid mistake by me. The components of a constant vector in spherical coordinates do depend on the coordinates, obviously. Thanks! $\endgroup$
    – Lior
    Mar 8, 2014 at 8:42

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