Question : Find curl of r^n vec(r) Solution : We shall Find curl of r^n vec(r) We know that \[\nabla=\hat{i}\frac{\partial}{\partial x}+\hat{j}\frac{\partial}{\partialy}+\hat{k}\frac{\partial}{\partialz}\] And \[r^n\vec{r}\ =r^n\left(x\hat{i}+y\hat{j}+z\hat{k}\right)=r^nx\hat{i}+r^ny\hat{j}+r^nz\hat{k}\] Therefore curl of r^n vec(r) is \[\nabla\times\left(r^n\vec{r}\right)=\left|\begin{matrix}\hat{i}&\hat{j}&\hat{k}\\\frac{\partial}{\partial x}&\frac{\partial}{\partial y}&\frac{\partial}{\partial z}\\r^nx&\ r^ny&\ r^nz\\\end{matrix}\right|\] \[=\hat{i}\left(\frac{\partial\left(\ r^nz\right)}{\partial y}-\frac{\partial\left(r^ny\right)}{\partial z}\right)-\hat{j}\left(\frac{\partial\left(\…
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