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Finding an electric field from a scalar field

  1. Nov 13, 2005 #1
    Say I know an electric field

    E = (yz - 2x)x-hat + (xz)y-hat + (xy)z-hat

    How do I find the scalar field that would produce that? If I integrate each part I get

    Vx = xyz - x^2
    Vy = xyz
    Vz = xyz

    Vt = 3xy - x^2

    To find E, I would take E = gradient cross the scalar field, but that would clearly not work. What I am doing wrong?
  2. jcsd
  3. Nov 13, 2005 #2

    Physics Monkey

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    Pick any component you want and integrate. For instance, if you picked the x-component then your guess "answer" would look like [tex] V = xyz - x^2 + f(y,z), [/tex] where f is an arbitrary function of y and z. This is because you only know that the partial derivative of V with respect to x is equal to yz - 2x. To figure out what your function f is, make use of your information about the other two partial derivatives of V. Of course, V is still undefined up to a constant.
  4. Nov 13, 2005 #3


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    Each component of the E-Field is the (-) derivitive of the scalar potential with THAT coordinate , yes E is the (-) gradient .

    Notice that d(x^2)/dy = 0 , so that E_y cannot give info about purely "x" terms in V, (or x and z terms, either). Similarly, E_x gives no info about purely y or z terms.

    Don't add the xyz terms, just make sure they all agree.
    Last edited: Nov 13, 2005
  5. Nov 13, 2005 #4
    Im still fuzzy on how to obtain the unknown function. Can you further explain?
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