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Finding the Electrical Field from the Electric Potential

  1. Feb 22, 2006 #1
    I am trying to solve this problem:

    The electric potential in a region of space is V = 210x^2 - 270y^2, where x and y are in meters. Find the E-field at (3m, 1m)

    So I started with:

    [tex]E = \frac{V}{d}[/tex]

    so then I plugged x and y into the electric potential equation and got

    V= -200 Volts

    Then I multiplied it by the distance [tex]d=\sqrt{x^2+y^2}[/tex]

    Unfortunately this is not the right answer. Perhaps someone could show me where I went wrong

    Thanks
     
  2. jcsd
  3. Feb 22, 2006 #2
    [tex]\vec{E}=-\vec{gradV}[/tex]
     
  4. Feb 22, 2006 #3
    what is [tex]\vec{gradV}[/tex]?
     
  5. Feb 22, 2006 #4
    If you used partial derivatives that would help you out.
     
  6. Feb 22, 2006 #5
    [tex]\vec{E} = -\vec{\nabla}V[/tex]


    [tex]\vec{\nabla} \equiv \frac{\partial}{\partial x} \hat{\mathbf{x}} + \frac{\partial}{\partial y} \hat{\mathbf{y}} + \frac{\partial}{\partial z} \hat{\mathbf{z}}[/tex]
     
    Last edited: Feb 22, 2006
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