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Question on Surface Integral and Flux

  1. Jan 15, 2015 #1
    1. The problem statement, all variables and given/known data
    I have a coordinate system, (x,y,z). There is a uniform-magnetic-field of 2.0 T that exists along
    the direction of the y-axis. There is a rectangular plane bounded by the points
    (3,0,0),(0,1,0),(0,1,1),(3,0,1).
    Calculate how much flux is traveling through the rectangular plane.

    2. Relevant equations
    Flux = B (dot) A (dot) d

    3. The attempt at a solution
    Since the rectangular plane is not changing, the magnetic-field is just dotted with the surface. And this surface is composed of the dot product of the Area and the Direction.

    I can easily find the area, but I don't know how to find the direction.

    What do I do with the information that tells me the B-field exists along the y-axis?
     
  2. jcsd
  3. Jan 15, 2015 #2

    gneill

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    Staff: Mentor

    Time to brush up on your linear algebra! From the points defining the plane you can construct two vectors that lie in the plane. Then think about how you might construct a vector that's perpendicular to them both.
     
  4. Jan 15, 2015 #3
    Would I compare triangles in the xy-plane?
     
  5. Jan 15, 2015 #4

    gneill

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    Staff: Mentor

    Nope. Review the cross product operation and what it gives you.
     
  6. Jan 15, 2015 #5
    Alright, so the corss product of two vectors will give me a vector that is perpendicular to the plane (which is in the direction that I want).

    I'm not sure what these vectors would be? How do I know what vectors to cross?
     
  7. Jan 15, 2015 #6

    jtbell

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    Staff: Mentor

    Any two vectors that lie in the plane should do, except if they're parallel (or antiparallel).
     
  8. Jan 15, 2015 #7
    Could I use, (3,-1,0)x(0,0,-1)?
     
  9. Jan 15, 2015 #8

    gneill

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    Staff: Mentor

    Yes, you could. See where that takes you. Beware of the fact that there are two normals to any plane (opposite directions).
     
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