# Divergence and Curl

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• Mar 29th 2008, 12:19 AM
marz_cro
Divergence and Curl
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!!!
• Mar 29th 2008, 03:22 AM
mr fantastic
Quote:

Originally Posted by marz_cro
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 .......