b$)$ A constant current flows in a thin closed loop. Use the generating function

$\frac{1}{|r-r^{\text{'}}|}=\frac{1}{r}{\displaystyle \underset{n=0}{\overset{}{}}}(\frac{r^{\text{'}}}{r}{)}^n{P}_n(cos)$

where $$ is the angle between the vectors $r$ and $r^{\text{'}},$ to show that the magneticmonopole contribution to the vector potential $A$ is zero.