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Derive the divergence formula for spherical coordinates
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[QUOTE="vanhees71, post: 4495728, member: 260864"] The idea is, however, correct. You can apply [tex]\int_{\Delta V} \mathrm{d}^3 \vec{x} \; \vec{\nabla} \cdot \vec{f} = \int_{\partial \Delta V} \mathrm{d}^2 \vec{A} \cdot \vec{f}[/tex] to an infinitesimal volume [itex]\Delta V[/itex] spanned by coordinate lines. On the left-hand side you can just take [itex]\vec{\nabla} \cdot{\vec{f}} \, \Delta V[/itex]. On the right-hand side, you must be a bit more careful and have to apply the changes of the arguments of [itex]\vec{f}[/itex] on the 6 surfaces into account. Only then all three differentials in the volume element can be cancelled, and only then you get the correct formula for the divergence in spherical coordinates, which is correctly given in your problem statement. [/QUOTE]
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Derive the divergence formula for spherical coordinates
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