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Plotting a 3-d surface in spherical co-ordinates

  1. Jul 23, 2010 #1
    1. The problem statement, all variables and given/known data
    The following is an equation of a 3-d surface in spherical co-ordinates.
    r = f(theta,phi) = sin(theta)
    Plot it on 3-d space.
    2. Relevant equations
    r = [tex]\sqrt{x^2 + y^2 + z^2 }[/tex]
    theta = arccos (z/ [tex]\sqrt{x^2 + y^2 + z^2 }[/tex])

    3. The attempt at a solution
    I converted the equation of the surface into cartesian co-ordinates , and got the following equation of a 3-d surface

    (x^2 + y^2 + z^2)^2 = (x^2 + y^2)
    is the above equation in cartesian co-ordinates right ?
    and is it a right approach to plot it?

    I think the plot is as shown in image given below ,
    but how to arrive at the plot given below I am unable to think.Please help

    [PLAIN]http://img689.imageshack.us/img689/7079/capturevug.jpg [Broken]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 24, 2010 #2


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    The surface has axial symmetry around the z axis. What is the projection of the surface to the y=0 plane? You get the 3D surface by rotating this curve around z. What kind of curve is this?

    Last edited: Jul 24, 2010
  4. Jul 27, 2010 #3
    Thanks for helping me in visualising how to plot the curve.

    It is the radiation pattern of a Hertz Dipole Antenna.For more you can readhttp://books.google.co.in/books?id=...R K shevgaonkar&pg=PA379#v=onepage&q&f=false"from google books
    Last edited by a moderator: Apr 25, 2017
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