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Homework Help: Cylinder area element

  1. Feb 24, 2010 #1
    1. The problem statement, all variables and given/known data
    I am trying to calculate power dissipated over a cylindrical surface using poynting vector -
    [tex]\oint[/tex] ExH ds

    I know ds for a sphere is r^2 sin [tex]\theta[/tex] d[tex]\theta[/tex] d[tex]\phi[/tex]

    But now sure what ds is for a cylinder?

    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 24, 2010 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    It depends on which surface you are talking about. A closed cylinder has 3 surfaces; one curved surface and two flat circular end-caps. For the end-caps, [itex]dS=s ds d\phi[/itex]. While, for the curved surface, [itex]dS=s d\phi dz[/itex]. (Using [itex]\{s,\phi,z\}[/itex] for the cylindrical coordinates)

    Griffiths' Introduction to Electrodynamics derives the infinitesimal displacements ([itex]dl_s=ds[/itex], [itex]dl_\phi=s d\phi[/itex], [itex]dl_z=dz[/itex]) in cylindrical coordinates in section 1.4.2. And the author gives a brief discussion of how to obtain area elements from these infinitesimal displacements at the end of page 40 (3rd edition).
     
  4. Feb 24, 2010 #3
    Great. I am gonna go take a look at Griffith's right now.
     
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