1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cross product in cylindrical coordinates

  1. Apr 12, 2013 #1
    In my physics textbook we have
    [itex]d\vec{l}=\hat{z}dz[/itex]
    and then it says
    [itex]d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz[/itex]

    How so? What is [itex]\hat{z}\times\hat{R}[/itex]? If it is [itex]\hat{\phi}[/itex] then where does the sine come from?
     
  2. jcsd
  3. Apr 12, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Check the definition of cross product.
     
  4. Apr 12, 2013 #3
    If i use the fact that a X b = |a| |b| sin(theta) then I understand where the sine comes from, it this case it would also mean that z X R is in the φ direction if [itex]d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz[/itex] is correct.

    but when I compute z X R using the 3x3 matrix
    R φ z
    0 0 1
    1 0 0

    I get +φ, and there is no sine.
     
  5. Apr 12, 2013 #4
    Any idea what am I missing?
     
  6. Apr 13, 2013 #5

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You have a big advantage on anyone commenting here: You are pulling some equation from your (unnamed) physics textbook. How about showing us a little more information?
     
  7. Apr 13, 2013 #6
    It looks like [itex]\hat{z}[/itex] is a unit vector in the axial direction, [itex]\hat{\phi}[/itex] is a unit vector in the circumferential direction, [itex]\hat{R}[/itex] is a unit vector pointing from the origin in an arbitrary spatial direction, and [itex]\theta[/itex] is the angle between the unit vector [itex]\hat{R}[/itex] and the z axis.

    [tex]\hat{R}=\sin(\theta)\hat{r}+\cos(\theta)\hat{z}[/tex]

    where [itex]\hat{r}[/itex] is a unit vector in the radial coordinate direction.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Cross product in cylindrical coordinates
  1. Cross product (Replies: 2)

Loading...