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Magnetic force on the loop

  • #1

Homework Statement



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.
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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.

Homework Equations




The Attempt at a Solution


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Answers and Replies

  • #3
Simon Bridge
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Homework Helper
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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)## ?
 
  • #4
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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.


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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:
  • #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.
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