[UPSC IFoS 2025] Electromagnetic Theory (Q301, 5+10=15M)

(i) Show that the vector potential \vec{\text{A}} at the position defined by the vector \vec{\text{r}} in a uniform electric and magnetic field is \vec{\text{A}} = \frac{1}{2}(\vec{\text{B}} \times \vec{\text{r}}).

(ii) Find out the divergence and curl of the vector potential \vec{\text{A}}.