- #1
yanyan_leung
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I am reading the Griffiths about finding the curl of B using Biot-Savart Law. I do not understanding the step between equation (5.52) and (5.53) which finding the x components of the following:
(\boldsymbol{J}\cdot\nabla^{\prime})\dfrac{\hat{\xi}}{\xi^{2}}
where
\mathbf{\mathbf{\xi}}=\mathbf{r}-\mathbf{r}^{\prime}
I don't know why it said using product rule 5 in his book, can get the following result:
\left(\boldsymbol{J}\cdot\nabla^{\prime}\right)\dfrac{x-x^{\prime}}{\xi^{3}}=\nabla^{\prime}\cdot\left[\dfrac{(x-x^{\prime})}{\xi^{3}}\mathbf{J}\right]-\left(\dfrac{x-x^{\prime}}{\xi^{3}}\right)\left(\nabla^{\prime}\cdot\mathbf{J}\right)
Is there anyone know how to deduce this result?
(\boldsymbol{J}\cdot\nabla^{\prime})\dfrac{\hat{\xi}}{\xi^{2}}
where
\mathbf{\mathbf{\xi}}=\mathbf{r}-\mathbf{r}^{\prime}
I don't know why it said using product rule 5 in his book, can get the following result:
\left(\boldsymbol{J}\cdot\nabla^{\prime}\right)\dfrac{x-x^{\prime}}{\xi^{3}}=\nabla^{\prime}\cdot\left[\dfrac{(x-x^{\prime})}{\xi^{3}}\mathbf{J}\right]-\left(\dfrac{x-x^{\prime}}{\xi^{3}}\right)\left(\nabla^{\prime}\cdot\mathbf{J}\right)
Is there anyone know how to deduce this result?
