- #1
yungman
- 5,723
- 242
I want to verify:
[tex]\vec A=\hat R \frac{k}{R^2}\;\hbox{ where k is a constant.}[/tex]
[tex]\nabla\cdot\vec A=\frac{1}{R^2}\frac{\partial (R^2A_R)}{\partial R}+\frac{1}{R\sin\theta}\frac{\partial (A_{\theta}\sin\theta)}{\partial \theta}+\frac{1}{R\sin\theta}\frac{\partial A_{\phi}}{\partial \phi}[/tex]
[tex]\Rightarrow\;\nabla\cdot\vec A=\frac{1}{R^2}\frac{\partial \left(R^2\frac{k}{R^2}\right)}{\partial R}= \frac{1}{R^2}\frac{\partial k}{\partial R}=0[/tex]
[tex]\vec A=\hat R \frac{k}{R^2}\;\hbox{ where k is a constant.}[/tex]
[tex]\nabla\cdot\vec A=\frac{1}{R^2}\frac{\partial (R^2A_R)}{\partial R}+\frac{1}{R\sin\theta}\frac{\partial (A_{\theta}\sin\theta)}{\partial \theta}+\frac{1}{R\sin\theta}\frac{\partial A_{\phi}}{\partial \phi}[/tex]
[tex]\Rightarrow\;\nabla\cdot\vec A=\frac{1}{R^2}\frac{\partial \left(R^2\frac{k}{R^2}\right)}{\partial R}= \frac{1}{R^2}\frac{\partial k}{\partial R}=0[/tex]