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Electric field from potential and coordinate

  1. Feb 20, 2009 #1
    1. The problem statement, all variables and given/known data

    I am given V(x,y,z) = 3x^2 + 2y + 5 and I am given s = (5,3,1), so what is the electric field?

    2. Relevant equations
    V= Es

    3. The attempt at a solution
    I really have no idea. What I tried:

    Derivative of V(x,y,z) = 6x+2
    so E = 32 N/C?

    Really I just don't understand the math necessary. How is it done?
  2. jcsd
  3. Feb 21, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    What you really need to do is take the gradient of the potential function:

    [tex]E = - \nabla V[/tex]

    You'll find the components of the electric field by taking the partial derivative with respect to each variable. Thus the x-component of the field will be -6x.

    See: http://hyperphysics.phy-astr.gsu.edu/Hbase/gradi.html" [Broken]
    Last edited by a moderator: May 4, 2017
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