- #1
neutrino2063
- 7
- 0
Why is
[tex]\nabla\cdot\vec{A}=\frac{1}{r}\frac{\partial}{\partial r}(rA_{r})+\frac{1}{r}\frac{\partial}{\partial \theta}(A_{\theta})[/tex]
Where
[tex]\vec{A}=A_{r}\hat{r}+A_{\theta}\hat{\theta}[/tex]
And
[tex]\nabla=\hat{r}\frac{\partial}{\partial r}+\hat{\theta}\frac{1}{r}\frac{\partial}{\partial \theta}[/tex]
Instead of just:
[tex]\nabla\cdot\vec{A}=\frac{\partial}{\partial r}(A_{r})+\frac{1}{r}\frac{\partial}{\partial \theta}(A_{\theta})[/tex]
[tex]\nabla\cdot\vec{A}=\frac{1}{r}\frac{\partial}{\partial r}(rA_{r})+\frac{1}{r}\frac{\partial}{\partial \theta}(A_{\theta})[/tex]
Where
[tex]\vec{A}=A_{r}\hat{r}+A_{\theta}\hat{\theta}[/tex]
And
[tex]\nabla=\hat{r}\frac{\partial}{\partial r}+\hat{\theta}\frac{1}{r}\frac{\partial}{\partial \theta}[/tex]
Instead of just:
[tex]\nabla\cdot\vec{A}=\frac{\partial}{\partial r}(A_{r})+\frac{1}{r}\frac{\partial}{\partial \theta}(A_{\theta})[/tex]
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