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Electric Potential

  1. Oct 21, 2012 #1
    V(x,y,z) = (Vo).e^[(-k|z|)].cos(kx)

    Find the electric field everywhere. Sketch the electric field lines in the x − z plane.


    Attempt:

    ∂V/∂x = -Ex

    -Ex = -k(Vo).e^[(-k|z|)].sin(kx) Ex = k(Vo).e^[(-k|z|)].sin(kx)

    ---------------------------------------------
    -Ez = -(Vo).k.e^[(-k|z|)].cos(kx) if z >=0

    Ez = (Vo).k.e^[(-k|z|)].[cos(kx)] if z >=0

    --------------------------------------------
    -Ez = +(Vo).e^[(-k|z|)].cos(kx) if z<0

    Ez =(Vo).e^[(-k|z|)].[-cos(kx)]


    My problem is sketching the electric field lines. Any tips?
     
    Last edited: Oct 21, 2012
  2. jcsd
  3. Oct 21, 2012 #2
    Your derivatives are wrong.
    You're missing a factor of k in the x term. You don't use the product rule in z.
     
  4. Oct 21, 2012 #3
    I was confounding z with k that's why i used the product rule :)

    But even with that equations i don't now how to sketch the lines :/
     
    Last edited: Oct 21, 2012
  5. Oct 21, 2012 #4
    As for plotting, try starting at any "obvious" points and paths. For example z=0, x=±nπ/2.
     
  6. Oct 21, 2012 #5
    Also consider how the field behaves as z→±∞
     
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