1. Not finding help here? Sign up for a free 30min 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!

Projection of surface area elements in vector calculus

  1. Mar 29, 2013 #1
    1. The problem statement, all variables and given/known data
    (i) Find the normal, n, at a general point on the surface S1 given by; x2+y2+z = 1 and z > 0.

    (ii) Use n to relate the size dS of the area element at a point on the surface S1 to its
    projection dxdy in the xy-plane.

    3. The attempt at a solution

    To find n initially I have just done the grad giving 2x,2y,1

    Then with the projection of the surface element I have done that dS=[itex]\hat{n}[/itex]dS and in this case because it is the xy plane it is just in the [itex]\hat{k}[/itex] direction.

    [itex]\hat{n}[/itex]=[itex]\frac{1}{\sqrt{1+4x+4y}}[/itex]

    and so I thought dxdy=[itex]\frac{dS}{\sqrt{1+4x+4y}}[/itex]

    I'm really not sure about this so and pointers would be a great help, thanks.

    Also, sorry about the poor LaTeX!
     
  2. jcsd
  3. Mar 29, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I think I'm following you here, but I'm not sure what your two "it"s are referring to.

    This is just the k-component of ##\hat{n}##, right?
    Check your normalization factor here, it's not quite correct.
    Otherwise, I think you're on the right track.
     
  4. Mar 29, 2013 #3
    Yes sorry, wasn't being very clear, I did mean the k component of n hat there yes. Ok I see the problem with the normalisation factor there, should be 4x2 and 4y2, thank you very much!
     
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: Projection of surface area elements in vector calculus
  1. Surface areas (Replies: 1)

  2. Vector area (Replies: 5)

Loading...