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Question on Surface Integral and Flux

  • Thread starter Loppyfoot
  • Start date
  • #1
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Homework Statement


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.

Homework Equations


Flux = B (dot) A (dot) d

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?
 

Answers and Replies

  • #2
gneill
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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.
 
  • #3
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Would I compare triangles in the xy-plane?
 
  • #4
gneill
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Would I compare triangles in the xy-plane?
Nope. Review the cross product operation and what it gives you.
 
  • #5
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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?
 
  • #6
jtbell
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Any two vectors that lie in the plane should do, except if they're parallel (or antiparallel).
 
  • #7
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Could I use, (3,-1,0)x(0,0,-1)?
 
  • #8
gneill
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20,792
2,770
Could I use, (3,-1,0)x(0,0,-1)?
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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