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Homework Help: Magnetic field of long parallel straight wires

  1. Mar 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Two infinitely long parallel straight wires carry currents in the +- z direction as shwn in the figure below. Each wire is located on the x-axis a distance of a from the origin.

    a) Determine B as a function of y along the line x=0
    b) Sketch a graph of B vs. y along the line x=0, including all values of y.


    2. Relevant equations
    B=u0I/2PiR


    3. The attempt at a solution
    for part a i get u0I/PiR
    for part b as y increases, B decreases because they're inversely related?
     
  2. jcsd
  3. Mar 14, 2010 #2

    Redbelly98

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    Not quite. It looks like you're calculating B at the origin (x=y=0) only, but you need to find B all along the y-axis, as a function of y. So you should get some expression that has y in it.

    For this, you'll need to get part (a) done correctly first, then you can sketch the function you get for (a).
     
  4. Mar 14, 2010 #3
    well if one current is flowing in the +z direction and one is flowing in the -z direction the magnetic field is the following:

    B=μI/2∏ {[(-y/(x-a)²+y²)+(y/(x+a)²+y²)]ihat + [(x-a/(x-a)²+y²)+(x+a/(x+a)²+y²)]jhat

    If we let x equal 0 and reduce, we get B = μIa/∏(a²+y²)

    I just know this from the answer in the back of my book, and I have no idea how they get it. :(

    From this equation you can deduce the graph. As y goes to infinity it seems as if B goes to zero. Correct?
     
    Last edited: Mar 14, 2010
  5. Mar 15, 2010 #4

    Redbelly98

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    How about B due to a single wire, do you know that?
    Yes.
     
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