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Magnetic force on the loop

  1. Apr 13, 2016 #1
    1. The problem statement, all variables and given/known data

    Rigid contour of an isosceles triangle and a long line cable lie in a plane and are located in vacuum . Determine the intensity of the magnetic force F acting on the loop. Current I = 100 A.
    magnetic_Force.png
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    Correct answer:
    F = 386 mN.
    I am getting 2 mN.
    Notice that I found dS by splitting while triangle in two triangles.
    2. Relevant equations


    3. The attempt at a solution
    magnetic_Force_Copy.png
    upload gambar
     
  2. jcsd
  3. Apr 13, 2016 #2

    BiGyElLoWhAt

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  4. Apr 13, 2016 #3

    Simon Bridge

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    How is the derivative in the last line not zero?
    Does the magnetic flux through the loop change with time?

    In the problem description, the wire loop is not carrying a current.
    ds is a line element and dS is a surface element... not always clear which you intend.
    ie. The area element between x and x+dx, inside the triangle, is dS=2y(x)dx : y=(x-a)/2
    So dS=(x-a)dx ... that what you mean?
    Then: ##\vec B = \frac{\mu_0 I}{2\pi x}\hat k## and ##d\Phi = \vec B\cdot d\vec S##
    ... means the flux density $$\Phi = \frac{\mu_0 I}{2\pi}\int_a^{2a}\frac{x-a}{x}\text{d}x$$ ... which is where you ended up.

    What about ##\vec F= I\oint (d\vec s\times \vec B)## ?
     
  5. Apr 14, 2016 #4
    Untitled.png
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    You mean something like this , still I don't understand how there can be force on the loop if there is no current I flowing through loop.


    Untitled2.png
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    By the way I think I messed something up because a didn't cancle out in F.Guess because I didnt do the loop integral the right way
     
    Last edited: Apr 14, 2016
  6. Apr 14, 2016 #5
  7. Apr 16, 2016 #6
    Please guys help me I am trying to figure out the whole day how my solution is incorrect, in the solution there is mi zero * I^2 / (2*pi) [1/2 - ln2] and I am having 1 - ln2 in the brackers , where did he get that one half from.
    Untitled.png
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