diff options
Diffstat (limited to 'mindmap/magnetostatics.org')
| -rw-r--r-- | mindmap/magnetostatics.org | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/mindmap/magnetostatics.org b/mindmap/magnetostatics.org index ea763e7..dd9d172 100644 --- a/mindmap/magnetostatics.org +++ b/mindmap/magnetostatics.org @@ -56,7 +56,7 @@ Due to the [[id:2a543b79-33a0-4bc8-bd1c-e4d693666aba][inverse square]] law, we k \begin{align*} \vec{\nabla} \times (\vec{J} \times \frac{\hat{r}}{r^{2}}) = 4\pi\vec{J}(\vec{r'})\delta(\vec{r}) + (\frac{\hat{r}}{r^{2}} \cdot \vec{\nabla})\vec{J} - (\vec{J} \cdot \vec{\nabla})\frac{\hat{r}}{r^{2}} \end{align*} -The first directional derivative is zero because $\vec{J}$ does not depend on the same coordinates as $\vec{\nabla}}$ +The first directional derivative is zero because $\vec{J}$ does not depend on the same coordinates as $\vec{\nabla}$ with the same reasoning as for the divergence, so we have: \begin{align*} \vec{\nabla} \times (\vec{J} \times \frac{\hat{r}}{r^{2}}) = 4\pi\vec{J}(\vec{r'})\delta(\vec{r}) - (\vec{J} \cdot \vec{\nabla})\frac{\hat{r}}{r^{2}} |