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Calculate net charge with nonuniform electric field

  1. Sep 4, 2016 #1
    1. The problem statement, all variables and given/known data
    In a cubical volume, 1.05 m on a side, the electric field is given by the formula below, where E0 = 1.25 N/C and a = 1.05 m.

    boldE.gif = E0(1 + z/a) i + E0(z/a) j

    The cube has its sides parallel to the coordinate axes, see the figure. Determine the net charge within the cube.

    22-43.gif


    2. Relevant equations

    φe = ∫E⋅dA = qenc0

    3. The attempt at a solution

    So I know that I need to calculate the net flux through all the 6 faces of the cube in order to solve for qenc. I know that φ+z and φ-z are equal to 0.

    I think I am doing something wrong because it seems like they would cancel out?

    φ+x = E0 a2 ∫ (1+z/a) dz
    φ-x = -E0 a2 ∫ (1+z/a) dz
    φ+y = E0 a2 ∫ (z/a) dz
    φ-y = -E0 a2 ∫ (z/a) dz

    Also, I would evaluate the integrals from 0 to a right?
     
    Last edited: Sep 4, 2016
  2. jcsd
  3. Sep 4, 2016 #2

    SammyS

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    You have done a lot correct.

    The units will be wrong.

    Where does a2 come from ?
     
  4. Sep 4, 2016 #3
    Hello!

    Yes.
    You don't think this is possible? Notice that for a particular ##z##, ##E## remains constant throughout the object. Also, what is the definition of flux?
     
  5. Sep 4, 2016 #4
    I think I was getting confused between ∫ E⋅dA and E⋅A, but since I'm doing the integral one then I don't need a2. So,

    φ+x = E0 ∫ (1+z/a) dz
    φ-x = -E0 ∫ (1+z/a) dz
    φ+y = E0 ∫ (z/a) dz
    φ-y = -E0 ∫ (z/a) dz

    from 0 to a.
     
  6. Sep 4, 2016 #5

    SammyS

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    The units are also incorrect this time.

    You need to integrate over y for some & over x for others. Since E is independent of x & y the result of those is easy.
     
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