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Gauss' Law Cube w/ 3D vector?

  1. Feb 14, 2010 #1
    I have a cube with sides l and therfore a total volume of l^3. The E-field is ax + by + cz where a, b, and c are known constants. It says to find the total E-field. The answer is (a + b + c)*l^3. I have no idea how they get this. I tried summing up all of the sides separately bit I kept getting zero. I understand why it is zero and do not understand the answer in the book. How do you do it? Thanks for the help!
     
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  3. Feb 14, 2010 #2

    kuruman

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    The direction of the electric field is very important. What is that direction?

    I thought you knew what the E-field is. What does "it" really say you should find?
     
  4. Feb 14, 2010 #3
    Sorry my mistake. It says to find the total flux through the cube. The direction of the E-field is simply the function i gave you with positive x, y, and z axes.
     
  5. Feb 14, 2010 #4

    kuruman

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    The function you posted appears to be a scalar function with no direction attached to it.
     
  6. Feb 14, 2010 #5

    ideasrule

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    Oh, so it has component a is the x direction, component b in the y direction, and component c in the z direction? If that's the case, then I agree, total flux has to be zero.
     
  7. Feb 14, 2010 #6
    ax (positive x) + by (positive y) + cz (positive z)
    apex is at (0,0,0)
    another apex at (L,0,0) & (0,L,0) & (0,0,L) etc.
     
  8. Feb 14, 2010 #7

    ideasrule

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    Now we're getting somewhere. Try calculating the flux in each direction (x,y,z), then adding them together vectorially to get the answer.
     
  9. Feb 14, 2010 #8

    kuruman

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    I guess you mean

    [tex]\vec{E}=ax\hat{x}+by\hat{y}+cz\hat{z}[/tex]

    As ideasrule said, calculate the flux through each face separately, remembering that the normal to the surface is always outward.
     
  10. Feb 14, 2010 #9
    And that's when I get zero
     
  11. Feb 15, 2010 #10

    kuruman

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    Can you show exactly how you get zero? Consider the two faces at x = +l and x = -l.
     
  12. Feb 15, 2010 #11
    sorry the corner is at the origin. I got it. I wasn't plugging in the coordinates once I integrated. Three of the sides have a flux of zero b/c they lie on some line. Thanks for the help and sorry for being so confusing!
     
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