Question Number 224732 by fantastic last updated on 30/Sep/25
$${The}\:{value}\:{of}\:{n}\:{for}\:{which}\:{the}\:{divergence} \\ $$$${of}\:{the}\:{function} \\ $$$$\mathrm{F}=\frac{\mathrm{r}}{\begin{vmatrix}{\mathrm{r}}\end{vmatrix}^{{n}} },\:\mathrm{r}=\mathrm{x}\hat {\mathrm{i}}+{y}\hat {\mathrm{j}}+{z}\hat {\mathrm{k}},\begin{vmatrix}{\mathrm{r}}\end{vmatrix}\neq\mathrm{0}, \\ $$$${vanishes}\:{is} \\ $$$$\left.{a}\right)\mathrm{1} \\ $$$$\left.{b}\right)−\mathrm{1} \\ $$$$\left.{c}\right)\mathrm{3} \\ $$$$\left.{d}\right)−\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{p}=\mathrm{38} \\ $$