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I How to write a Vector Field in Cylindrical Co-ordinates?

  1. Oct 31, 2016 #1
    Ethetahat.jpg
    Let's say we have a vector field that looks similar to this. Assume that the above image is of the x-y plane.

    The vector arrows circulate a central axis, you can think of them as tangents to circles.

    The field does not depend on the height z.

    The lengths of the arrows is a function of their radial distance from the center/axis, f(r).


    How do we write this vector field in terms of Cylindrical coordinates?
    ##A_\rho \hat{\boldsymbol \rho} + A_\varphi \hat{\boldsymbol \varphi} + A_z \hat{\mathbf z}##

    How does one find ##A_\rho , A_\varphi## and ##A_z ## ?
     
  2. jcsd
  3. Oct 31, 2016 #2
    Vector V = (Aφ)* unit vector φ, where Aφ = f(ρ) with Aρ = 0 and Aρ = 0 and Az = 0
     
  4. Oct 31, 2016 #3
    thanks!

    But what do you mean by "with Aρ = 0"?

    Also, can you describe how the cylindrical unit vectors work? You can post a link if you like.
     
  5. Oct 31, 2016 #4
    Aρ = 0 and Az = 0 means the component of the vector field along ρ unit vector and along z unit vector both are zero.In other words vector field every where is perpendicular to ρ unit vector and z unit vector and is entirely along unit vector φ.
     
    Last edited: Oct 31, 2016
  6. Oct 31, 2016 #5
    thanks, that was a great simple explanation.
     
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