Gauss's Law- Flux through surface

  1. 1. The problem statement, all variables and given/known data
    A flat surface with area .14 m^2 lies in the x-y plane, in a uniform electric field given by E=5.1i +2.1j+3.5k kN/C.
    A) Find the flux through the surface.


    2. Relevant equations
    Flux = E dot A (Vector math?)



    3. The attempt at a solution
    I believe this is the dot product of two vectors. Converting the surface area to vectors (i,j,k) I come up with (.374i, .374j, 0k). When I calculate the dot product:
    (5100, 2100, 3500) (.374, .374, 0) I get 2694 N M^2/C (wrong). I believe the plane vectors are incorrect. Guidance please?

    Thanks again.
    Chip
     
  2. jcsd
  3. What is the definition of an area vector, [tex] \vec{A} [/tex]? This is where you are having trouble.
     
  4. Thank you for the push in the direction. I understand I have to convert the area into a vector. I have been looking through my old notes and texts on this subject. Since the area is assumed to be flat (no 'z' (k) component), I assumed zero for that value. I took the square root of .14 m^2 (oops) .... I think this is where I made my mistake.
    Will forge ahead!
     
  5. Ok, with this problem, I am obtaining the dot product of the two vectors. I believe the vector for the 'plane' would be N= [.14 + .14 + 1]
    When I do the dot product as follows:
    Ex*Nx + Ey*Ny + Ez*Nz = # NM^2/C

    5100*.14 + 2100*.14+3500*1 = 4508 N M^2/C for the flux through the surface. This is wrong though. Another nudge please?

    Thank you.
    Chip
     
  6. According to your most recent response, your definition of the area vector is still not correct. See the link: http://en.wikipedia.org/wiki/Vector_area
    According to this problem, there is only one nonzero component of the area vector.
     
    Last edited: Feb 8, 2009
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