# Converting to cylindrical and then taking div and curl

1. Feb 22, 2008

### EngageEngage

1. The problem statement, all variables and given/known data
Change to cylindrical coordinates and find the divergence

F = <x, y, 0>/(x^2 + y^2)

2. Relevant equations

$$\nabla$$ . F = $$\frac{1}{\rho}$$$$\frac{\partial\rho F}{\partial\rho}$$+$$\frac{1}{\rho}$$$$\frac{\partial F}{\partial\theta}$$+$$\frac{\partial F}{\partial z}$$

3. The attempt at a solution

i changed into cylindrical by simply having x = $$\rho$$cos$$\theta$$
y =$$\rho$$sin$$\theta$$ and x^2 +y^2 = $$\rho$$^2. THen, using the above formula I get cos(theta)/rho^2. The answer is 0 however. Can someone please tell me what i could have messed up?

2. Feb 22, 2008

### EngageEngage

Wait, must I also convert the i,j,k unit vectors to e(rho), e(theta), and ez before I can use vector operations? If i do this i get the right answer, but I'm still not sure -- my book doesn't have a single example excersise so I dont have too much to work off of. If someone could help me out that would be appreciated greatly. Thank you

3. Feb 22, 2008

### Dick

Sure. You have to convert the basis vectors as well. You should get F_r=1/r and the other components zero, so div(F)=0.

4. Feb 22, 2008

### EngageEngage

that is in fact what I got. Thank you very much for the help -- unfortunately my book offers only theory and no examples.