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Magnetic Field of two wires

  1. May 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Two long thin parallel wires a distance d = 15.3 cm apart carry 25-A currents (I) in the same direction. The magnetic field is measured at point P, a distance d1 = 13.3 cm from the lower wire and a distance d2 = 5.3 cm from the upper wire.

    a. Find the x and y components of the magnetic field at P due to the current in the lower wire only.
    HELP: First find the magnitude of the field due to the current in the lower wire.
    HELP: To find the direction of the field, the Law of Cosines will be helpful: for a triangle of sides a, b, and c, the angle θ between sides a and b is given by c2 = a2 + b2 - 2 a b cosθ.

    https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/Knox/phys130a/spring/homework/13/04/HW14_4.jpg [Broken]
    2. Relevant equations
    c2 = a2 + b2 - 2 a b cosθ.
    Magnitude=[tex]\mu[/tex]0I/2[tex]\pi[/tex]r



    3. The attempt at a solution
    So I found the magnitude to be [tex]\mu[/tex]0(25)/2[tex]\pi[/tex](.133)=3.759E-5
    then I use the Law of Cosines to find that theta=19.814
    so then 90-19.814=70.186
    Cos of that= y/3.759e-5
    which gives me y=1.274e-5
    Which is correct.
    However, when I use Sin of 70.186=x/3.759e-5 I get 3.536e-5, but this is not correct. I'm not sure what I'm doing wrong here. :/ I've never quite understand how to tell when you use Sin and Cos for which value anyway.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 10, 2009 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Your work looks pretty good, so I imagine the problem is one of the following:

    Wrong number of significant figures in final answer,
    Final answer slightly wrong from roundoff error,
    or
    +/- Sign error in final answer.

    In your diagram, have you drawn the direction of B due to the lower wire? That might help clear up whether it's + or -.
     
  4. May 10, 2009 #3
    I didn't even think about the fact that it could be negative. B is going anti-clockwise, so it's negative. Thanks!
     
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