Solution
= Solution
Take the <curl> of the integral from part (a). Since $J(r')$ is independent of $r$,
$$
\begin{aligned}
B(r)&=\nabla\times A(r)\\
&=\frac{\mu_0}{4\pi}\int
\nabla\!\left(\frac1{|r-r'|}\right)\times J(r')\,d^3r'\\
&=\frac{\mu_0}{4\pi}\int
\frac{J(r')\times(r-r')}{|r-r'|^3}\,d^3r'.
\end{aligned}
$$
This is the <Biot-Savart law>.