Force exerted by a magnetic field

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Homework Statement


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.


Homework Equations


F=I(LxB)

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?
 

Answers and Replies

  • #2
collinsmark
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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?

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 \\
\end{tabular}
\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.
 
  • #3
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Yes I did mean the cross product. Thank you very much this helped a lot!
 

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