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Homework Help: Electric Field via partial derivative

  1. Mar 21, 2012 #1
    1. The problem statement, all variables and given/known data
    The electric potential in a certain region of space is given by: V(x,y,z) = 1000x-2000y-1500z(Volts). a.)Find the electric field corresponding to the given electric potential. Draw some electric field lines. b.) What charge distribution can create this electric field? Give all possible numericical information about the charge distribution that you can find from the given data.

    2. Relevant equations
    V=dv dv=-E*dl
    dv(x,y,z) = ∂v/∂x *dx + ∂v/∂y *dy + ∂v/∂z *dz

    E*dl = Exdx+Eydy+Ezdz

    Ex = - ∂v/∂x Ey = - ∂v/∂y Ez = - ∂v/∂z

    3. The attempt at a solution
    V(x,y,z) = 1000x-2000y-1500z
    dv = 1000-2000-1500
    Ex = -1000 Ey = 2000 Ez = 1500

    I have a gut feeling that I am missing some rather important steps here. I also have no idea where to begin in terms of drawing this, any help is highly appreciated.
  2. jcsd
  3. Mar 22, 2012 #2


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    welcome to pf!

    hi fornax! welcome to pf! :smile:
    yes, that looks ok :smile:

    (sometimes, the first part of an exam question is deliberately easy! :wink:)

    now select a few random points, and draw arrows to show the magnitude and direction of the force (the field) …

    what's the pattern? ​
  4. Mar 22, 2012 #3
    I haven't worked with these much, so just put in any value in place of the Ex Ey, Ez? If I had to make an educated guess right now, I would say all of the vectors are pointingtoward the left, up and out of the screen, or page. As far as the charge distribution, it would have to be an infinite sheet, correct? Especialy since the field remains constant...
  5. Mar 22, 2012 #4


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    yes :smile:

    to put it simply, the E field is constant, so the lines are parallel

    it doesn't have to be an infinite sheet

    (they are quite difficult to buy! :biggrin:)

    the question says "a certain region", so you only need something small …

    can you think of something you could buy that does have a uniform field in a small region? :wink:
  6. Mar 22, 2012 #5
    that's pretty easy, a capacitor. Now to find "all possible numerical information", I just backtrack, with each individual component?

    ie. Ex = σ/ 2ε0

    -1000 = σ/ 2ε0

    σ = -5.7x10^13
  7. Mar 22, 2012 #6


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    uhh? how many capacitors are you using?? :confused:

    i] which direction will the capacitor have to face?

    ii] what is the magnitude of the electric field?

    iii] so what is the surface charge density? :smile:
  8. Mar 22, 2012 #7

    It would have to be facing in the direction of the E field, so that it's face is perpindicular to the E field.

    [ii] llVll = √(x2 + y2 + z2
    llVll = √-10002 + 20002 + 15002
    llVll = √7250000
    llVll = 2693

    so then


    E = σ/ 2ε0

    2693 = σ/ 2ε0

    σ = 4.76 x 10-8 C/m2

    that seems too low :/
  9. Mar 22, 2012 #8


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    shouldn't it be E = σ/ε0 ?
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