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Force Due to Magnetic Field on a Charge Carrying Wire

  1. Jun 25, 2008 #1
    Hi, I have a bit of a problem understanding one of the solutions for my assignment.
    1. The problem statement, all variables and given/known data
    Normally we use the equation
    F = iL X B
    to find the force of a magnetic field on a wire with a current.

    One of the questions asks to find the force on a section of wire between x=3 and x= 1, the wire's current is in the the negative x direction. The magnetic field is something like B=3i+8.0x^2

    They used integration to solve the problem, integrating the change of force from 1 to 3. I'm wondering why this is used? Is it because the magnetic field is not uniform (it's in terms of x)? If the magnetic field is uniform, could we just have done F = iL x B with 2 being the L?

    Thanks in advance!
  2. jcsd
  3. Jun 25, 2008 #2


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    Homework Helper

    Is the magnetic field supposed to be B = 3i + 8.0x^2j?

    If that's the case, then, yes, the field is not uniform over the section x = 3 to x = 1, so an integration is necessary over the length of the wire.
  4. Jun 26, 2008 #3
    You can only use [tex]\vec{F} = I (\vec{L} \times \vec{B})[/tex] when the magnetic field is constant. Since here, your magnetic field is different over a particular area, you have to use integration.
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