# Recast a given vector field F in cylindrical coordinates

1. Feb 26, 2017

### Bestphysics112

1. The problem statement, all variables and given/known data
F(x,y,z) = xzi

2. Relevant equations
N/A

3. The attempt at a solution
I just said that x = rcos(θ) so F(r,θ,z) = rcos(θ)z. Is this correct? Beaucse I am also asked to find curl of F in Cartesian coordinates and compare to curl of F in cylindrical coordinates. For Curl of F in cylindrical coordinates I obtained rcos(θ)eθ+sin(θ)zez. This doesn't look anything like the curl found in Cartesian coordinates. Where am i going wrong?

2. Feb 26, 2017

The unit vector $\hat{i}$ also needs to be put in cylindrical coordinates. $\hat{i}=cos(\theta) \hat{a}_r -sin(\theta) \hat{a}_{\theta}$ if I computed it correctly. Once you do that, you should get agreement when you do the curl operation in cylindrical coordinates. $\\$ Editing: Yes, I computed it, and got agreement. I'd be happy to check the answer for you that you get.

Last edited: Feb 26, 2017
3. Feb 26, 2017

### Bestphysics112

Hello! Sorry I just saw this reply. As an answer, I got (rcos(θ)sin(θ)er +rcos2(θ)eθ +(2cos(θ)sin(θ)z+ 2sin(θ)cos(θ)z)ez

Edit- Yes! I figured out my mistake and I got an equivalent answer. Thank you for the help Charles

Last edited: Feb 26, 2017
4. Feb 27, 2017

Please check your $e_z$ term. The first term gets a minus sign so that the $e_z$ term is zero. Also what did you get in Cartesian coordinates for the curl? The two should agree and I think they do if the $e_z$ term is zero.