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Biot Savart Law Problem

  1. Apr 29, 2016 #1
    1. The problem statement, all variables and given/known data
    The figure shows two very long straight wires (in cross section) that each carry a current of 3.19 A directly out of the page. Distance d1 = 6.00 m and distance d2 = 4.00 m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires?
    HW9Q7.png


    2. Relevant equations
    Biot-Savart's Law


    3. The attempt at a solution
    [itex]{ B }_{ long,\quad straight\quad wire }\quad =\quad \frac { { \mu }_{ 0 }I }{ 2\pi r } \\ r\quad =\quad \sqrt { { (\frac { { d }_{ 1 } }{ 2 } ) }^{ 2 }\quad +\quad { { d }_{ 2 } }^{ 2 } } \\ { B }_{ total }\quad =\quad 2B\quad =\quad \frac { { \mu }_{ 0 }I }{ \pi r } \\ { B }_{ total }\quad =\quad 1.7695e-07[/itex]

    I'm aware that I'm missing a sin(theta) in my multiplication, but why would I need to only specify a vertical component? The magnitude isn't only the vertical component.
     
  2. jcsd
  3. Apr 29, 2016 #2

    TSny

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    What is the direction of B for each current?
     
  4. Apr 29, 2016 #3
    Both act upwards on the point
     
  5. Apr 29, 2016 #4

    TSny

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    The two fields at P are not in the same direction.
     
  6. Apr 29, 2016 #5
    Is this what you're visualizing:
    Upper field points in the positive x and y direction
    Lower field points in the negative x but positive y direction
    ?
     
  7. Apr 29, 2016 #6

    TSny

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    Yes.
     
  8. Apr 29, 2016 #7
    Alright that makes sense now to put the y component in. I was visualizing both fields pointing up at the same time, but that's not possible at all with the orientation of the field.
     
  9. Apr 29, 2016 #8

    TSny

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    OK.
     
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