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Computing for Electric Field given cylindrical coordinates of v.

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data

    If the scalar electric potential v in some region is given in cylindrical coordinates by
    [itex] v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}} [/itex], what is the electric field [itex] \vec{E}[/itex] in that region?

    2. Relevant equations

    [itex] E = -\nabla v [/itex]

    3. The attempt at a solution

    So, first I need to change the cylindrical coordinates to cartesian coordinates.

    [itex] v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}} [/itex]

    [itex] v (r, \phi, z) = (x^2 + y^2) \frac{y}{r} e^{\frac{-3}{z}} [/itex]

    [itex] v (r, \phi, z) = (x^2 + y^2) \frac{y}{\sqrt{x^2 + y^2}} e^{\frac{-3}{z}} [/itex]

    [itex] v (r, \phi, z) = y e^{\frac{-3}{z}} \sqrt{x^2 + y^2} [/itex]

    ** so is this already the cartesian coordinates? can I perform the gradient now?
     
  2. jcsd
  3. Feb 7, 2012 #2

    vela

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  4. Feb 7, 2012 #3
    ow, I see. We were not given that formula though. So I think I need to do it in cartesian coordinates. Thanks.
     
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