# Int x' dV/|r-r'| ?

1. Mar 19, 2006

### Living_Dog

Int x' dV/|r-r'| !?!

The Helmholtz Theorem says that if
$$\nabla \circ \vec{F} = 0$$ and
$$\nabla \times \vec{F} = \vec{C}(\vec{r})$$ then
$$\vec{F} = \nabla \times \vec{A}$$ where
$$\vec{A} = \frac{1}{4\pi}\int\int\int\frac{\vec{C}(\vec{r}')}{\left|\vec{r} - \vec{r}'\right|}dx'dy'dz'$$

The problem gave $$\vec{F_1}=x^2\hat{z}$$.

The divergence of $$\vec{F}_1$$ is zero, and the curl of $$\vec{F}_1$$ is $$-2x\hat{y}$$.

My problem is finding the vector potential, $$\vec{A}$$. This looks like a monster to do since none of the integral tricks I know seem to work.

So any help on solving this would be very appreciated. Here is the integral:

$$A_y = \frac{1}{4\pi}\int\int\int \frac{2x'}{\left|\vec{r} - \vec{r}'\right|}dx'dy'dz'$$

thanks in advance!
-LD

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