# Tagged Questions

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### What is the relationship of the curl of a vector with its conservativeness? [on hold]

My Physics teacher told me that a conservative field has zero curl.But I am not getting the logic behind it...I am even not clear why the curl represents how much the vector field swirls around the ...
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### Gauss' Law for Magnetism Derivative Form: With or without volume integral?

I've been reading through FLP Vol. II, and he has proven that as the flux through a closed surface is: $\ \int_{surface} \mathbf{F} \space \mathrm{d}\mathbf{a}$, according to the divergence theorem, ...
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### Convective Operators: Cartesian vs Spherical Coordinates

(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 ...
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### Divergence of cross product of transverse component

If I define the vector as $V_i=V^T_i+V^L_i$ and the transverse part is defined by $$V^T_i=\Big(\delta_{ij}-\frac{\partial_i\partial_j}{\partial^2}\Big)V_j$$ then is is obvious that $\nabla.V^T=0$ as ...
### Divergence of $\frac{\hat{r}}{r^2}$
In David J. Griffiths's Introduction to Electrodynamics, the author gave the following problem in an exercise. Sketch the vector function $$\vec{v} ~=~ \frac{\hat{r}}{r^2},$$ and compute ...