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Magnetic field at the center of a loop

  1. Feb 19, 2015 #1
    1. The problem statement, all variables and given/known data
    upload_2015-2-19_11-57-30.png
    A conductor consists of a circular loop of radius
    R = 14.4 cm
    and two long, straight sections as shown in the figure. The wire lies in the plane of the paper and carries a current
    I = 1.60 A.
    Find the magnetic field at the center of the loop.

    2. Relevant equations
    biot-savart law
    ?

    3. The attempt at a solution
    I know I need use biot-savart law to get the field created by the loop, which is giving me 8.77 uT. This is apparently within 10% of the correct answer.
    Do i need to find the current from the straight part of the wire too (superposition)?

    I'm just not sure how to do this / what equations to use to do this?
     

    Attached Files:

  2. jcsd
  3. Feb 19, 2015 #2

    gneill

    User Avatar

    Staff: Mentor

    Yes. And superpostiion is an excellent idea.
    You should have an expression for the magnetic field at a given distance from a current-carrying wire...
     
  4. Feb 19, 2015 #3
    thats where i'm confused.

    shouldn't i use B = (uI)/(2 pi r) ?
    4pi x 10^-7 x 1.6A / 2 pi x .144m ? this gives me 2.22 uT which when added to the 8.77 is out the the correct range
     
    Last edited: Feb 19, 2015
  5. Feb 19, 2015 #4

    gneill

    User Avatar

    Staff: Mentor

    2.22 μT looks right for the straight wire. But the loop contribution looks a bit high to me. Can you show the details of your work there?
    No, the expression gives the field magnitude, not a differential element. The integration was already done in deriving the expression.
     
  6. Feb 19, 2015 #5
    Ahhhh thank you! my mistake was in the calculation for the loop! i left the 4pi in place when using u/4pi

    hahaah that was dumb. but thank you, i got the right answer. it's 9.20 uT!

    :)
     
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