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Homework Help: Force exerted by a magnetic field

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data
    a 10cm long straight wire is parallel with the z axis and carries a current of 4.0A in the +z direction. The force on this wire due to a uniform magnetic field B is -0.20N i+0.20N j. If this wire is rotated so that it is parallel with the x axis with the current in the +x direction, the force on the wire becomes 0.20N k. Find B.

    2. Relevant equations

    3. The attempt at a solution
    I rearranged the equation so B=F/(IxL). I plugged all of the numbers in but I dont understand how to do the dot product if I is not a vector. Can I use some kind of dot product between F and L?
  2. jcsd
  3. Feb 23, 2010 #2


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    Homework Helper
    Gold Member

    I think you mean cross product, but anyway...

    I think you can solve this problem by getting more detailed with what the cross product actually is.

    One of the equations you've listed is

    [tex] \vec F=I(\vec L \times \vec B) [/tex].

    Being more explicit with the cross product, this is the same thing as:

    [tex] \vec F = I\left( \left|
    \begin{tabular}{ l c r }
    i & j & k \\
    L_x & L_y & L_z \\
    B_x & B_y & B_z \\
    \right| \right) [/tex]

    where the thing inside of the parenthesis represents the determinant of the matrix.

    What makes this problem a lot easier, is that some of the L components are zero in the first case, and other components are zero in the second case. So even though it looks ugly now, it's actually pretty easy to generate a few equations to solve for Bx, By, and Bz.
  4. Feb 24, 2010 #3
    Yes I did mean the cross product. Thank you very much this helped a lot!
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