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Calculating magnetic force on circular coil carrying current

  1. Jan 26, 2015 #1
    1. The problem statement, all variables and given/known data
    A circular coil with center on the z axis and orthogonal to the xy axis carries a current. The coil is in a magnetic field B with axial simmetry compared to the x axis. B forms an angle θ with the z axis. Calculate the magnetic force acting on the coil.

    exerc.png

    2. Relevant equations

    $$\vec{F_B} = i \vec{dl} x \vec{B}$$

    3. The attempt at a solution

    I tried considering $$ dl = r d\phi $$
    So [itex]F = irB_zd\phi [/itex]
    where Bz is [itex]Bcos\theta[/itex]

    By is null because it has opposite verse on opposite points of the coil. So I can consider just Bz

    $$ F = irBcos\theta d\phi = irBcos\theta \int_0^{2\pi} d\phi = 2\pi irBcos\theta$$

    The result, according to the book, is [itex]2\pi irBsin\theta[/itex]
    Why?
     
  2. jcsd
  3. Jan 26, 2015 #2
    How does your book define ##\theta##? Is it the angle the magnetic field makes with the horizontal(i.e. ##B_y##)?
     
  4. Jan 26, 2015 #3
    It is the angle between B and Bz!
     
  5. Jan 27, 2015 #4

    rude man

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    What does this mean?
     
  6. Jan 27, 2015 #5
    I can't understand what does it mean, actually.
     
  7. Jan 27, 2015 #6

    rude man

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    So ask! The problem is not you, it's the instructor who can't write understandably!
     
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