- #1

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- Homework Statement
- I have a charge Q on a sphere at the origin. At t=0 the sphere explode and create a current density ##\vec{J}(\vec{r}) = J(r)\hat{r}##. I have to prove that ##B = \nabla \times A = 0## using ampere Maxwell law

- Relevant Equations
- ##\nabla \times B = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{d \vec{E}}{dt}##

##\vec{A}(\vec{r},t) = \frac{\mu_0}{4 \pi} \int \frac{\vec{J}(\vec{r}', t_r)}{|r - r'|} d \tau '##

##t_r = t - \frac{|r - r'|}{c}##

Since I have to use Ampere-Maxwell equation I don't see how to begin the problem. I don't know how to right hand side can be 0 and I don't see how to isolate ##\nabla \times A ## on the left hand side. Is it purely mathematic?