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Vector area sphere

  1. Apr 7, 2012 #1
    1. The problem statement, all variables and given/known data
    I wonna calculate the vector area dS of a sphere, but for some reason my result gets mixed areound. I need a trained eye to see where I make a silly mistake.


    2. Relevant equations
    Parametrization of a sphere:

    (x,y,z) = r(cos[itex]\phi[/itex]sin[itex]\theta[/itex],sin[itex]\phi[/itex]cos[itex]\theta[/itex],cosθ)

    3. The attempt at a solution
    So ∂r/∂[itex]\phi[/itex] = r(cosθcos[itex]\phi[/itex],-sinθsin[itex]\phi[/itex],sinθ)
    and
    ∂r/∂θ = r(-sin[itex]\phi[/itex]sinθ,cos[itex]\phi[/itex]sinθ,0)

    and dS = ∂r/∂[itex]\phi[/itex] x ∂r/∂θ = r2 (sinθcosθcos[itex]\phi[/itex],sin[itex]\phi[/itex]sinθ2, ......) dθd[itex]\phi[/itex]

    But the first two terms should be switched around according to my notes! Where do I go wrong? :(
     
  2. jcsd
  3. Apr 7, 2012 #2

    LCKurtz

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    Well, you have the ##\theta## and ##\phi## reversed from the usual math notation for spherical coordinates, but I guess some physicists do that. But when you differentiated with respect to ##\phi## it looks like you differentiated the ##\theta## variables, and conversely.
     
  4. Apr 7, 2012 #3
    nvm.. Found my mistake - the parametric equation was wrong.
     
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