Hey guys ive been asked to calculate the divergence and curl of the vector function:
V(x,y,z)= (xi + yj + zk)/r^2
where r^2=(x^2)+(y^2)+(z^2)
Any help would be great i dont know where to begin with this one!!!
How about beginning by looking at the definitions? What do they suggest you need to do ....?
Finding $\displaystyle \frac{\partial V_1}{\partial x}$ is hackwork much better left for you to do. But once found, you can use symmetry to easily write down:
$\displaystyle \frac{\partial V_2}{\partial y}$ (just swap x and y around in your answer for $\displaystyle \frac{\partial V_1}{\partial x}$), and
$\displaystyle \frac{\partial V_3}{\partial z}$ (just swap x and z around in your answer for $\displaystyle \frac{\partial V_1}{\partial x}$).
Of course, you could always recognise that $\displaystyle \boldsymbol{V} = \frac{\boldsymbol{r}}{r^2} = \frac{\hat{\boldsymbol{r}}}{r}$ and find div and curl in an appropriate alternative coordinate system ...
PS. I assume you're OK with the level curve question doing the rounds from this assignment .......