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Magnetic Field of Two Wires

  1. Feb 20, 2009 #1
    Two wires carry current I1 = 49 A and I2 = 31 A in the opposite directions parallel to the x-axis at y1 = 7 cm and y2 = 15 cm. Where on the y-axis (in cm) is the magnetic field zero?


    I dont even know where to start on this. Any help would be great!
     
  2. jcsd
  3. Feb 20, 2009 #2

    LowlyPion

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    Consider the magnetic field of a wire carrying current:
    where (+) is going into the page, and (.) is coming up out of the page.

    (+) (+) (+) (+) (+) (+)
    ------------------------>
    (.) (.) (.) (.) (.) (.)

    If you add one going the other direction then:

    (+) (+) (+) (+) (+) (+)
    ------------------------>
    (.) (.) (.) (.) (.) (.)

    (.) (.) (.) (.) (.) (.)
    <------------------------
    (+) (+) (+) (+) (+) (+)

    So in between the fields reinforce. Which means to either side they may cancel somewhere - which is what you want.

    With the B field given by B = μo*I/2π*R you need to construct an equation that describes where the fields are equal but opposite.
     
  4. Feb 20, 2009 #3
    Well originally I was thinking μo*I1/2π*R = - μo*I2/2π*R, but I know this is wrong. Then I considered I1/R1 = - I2/R2, but I dont think this is right either....so im still lost
     
  5. Feb 20, 2009 #4

    LowlyPion

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    You need to pick some location call it P outside the 2 wires. It will be a distance of D away from one wire and D + 8 cm away from the other. Now what you need to do is find where the fields are equal.

    Use that in your I1/R1 = I2/R2
     
  6. Feb 20, 2009 #5
    So say I pick P as Y = 17, so that point would be 2cm away from wire 1 and 10 cm away from wire 2...how do I use this information to find where the fields are equal?
     
  7. Feb 20, 2009 #6

    LowlyPion

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    No, no, no.

    Say you pick R1 as D and R2 as 8 cm + D, and then solve for what D is.
     
  8. Feb 20, 2009 #7
    Ok, so I did 49/D = 31/D+8 and solved for D...is this value supposed to be where on the Y axis the magnetic field is zero?
     
  9. Feb 20, 2009 #8

    LowlyPion

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    It's not the Y coordinate value. It's the distance from the 49A laden wire. You will have to make a drawing and determine what that y coordinate value would be.

    Note: Since you chose D as from the 49 you should expect that the (-) value you get is in the direction of the 31A wire and to the other side of it.
     
  10. Feb 20, 2009 #9
    I finally got it. Thank you so much for your help
     
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