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Recast a given vector field F in cylindrical coordinates

  1. Feb 26, 2017 #1
    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. jcsd
  3. Feb 26, 2017 #2

    Charles Link

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    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
  4. Feb 26, 2017 #3
    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

    Is this answer correct?

    Edit- Yes! I figured out my mistake and I got an equivalent answer. Thank you for the help Charles
     
    Last edited: Feb 26, 2017
  5. Feb 27, 2017 #4

    Charles Link

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    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.
     
  6. Feb 27, 2017 #5
    I don't have my homework with me, but I forgot to edit my post with the answer I got. The ez terms canceled
     
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