- #1
_Andreas
- 144
- 1
Homework Statement
Determine the vector [tex]\bm{B}=\left(\frac{\partial A_{\theta}}{\partial r}-\frac{1}{r}\frac{\partial A_r}{\partial \theta}\right)\hat{\phi}[/tex]
[tex]A_r[/tex] and [tex]A_{\theta}[/tex] are the components of the basis vectors [tex]\hat{r}[/tex] and [tex]\hat{\theta}[/tex].
The Attempt at a Solution
I just calculated the differentials in the expression for B above, but that gave me a factor [tex]1/r[/tex] too much in the answer. My textbook rewrites B as
[tex]\bm{B}=\frac{1}{r}\left(\frac{\partial (A_{\theta}r)}{\partial r}-\frac{\partial A_r}{\partial \theta}\right)\hat{\phi}[/tex].
They've broken out a factor [tex]1/r[/tex] before differentiating, but I don't understand the
[tex]\frac{\partial (A_{\theta}r)}{\partial r}[/tex]
part. Why isn't it
[tex]r\frac{\partial (A_{\theta})}{\partial r}[/tex]?