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Calculate the force on a particle from magnetic field of infinite wire

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Problem: Determine an expression for the magnitude of the magnetic force on a charged particle moving near an infinitely long wire, carrying a current i.
    • Particle with charge q
    • Magnitude of the particles velocity = |v|
    • Magnetic field strength = B
    • Current = i


    2. Relevant equations
    B can be calculated with:
    [itex]B=\frac{μ_{0}i}{2\pi{r}}[/itex]

    Magnitude of force can be calculated with:
    [itex]F=q*v*b*sin(θ)[/itex] (Cross product of the particles velocity vector and the magnetic field vector)

    3. The attempt at a solution
    I've combined these equations to come up with a single equation for the magnitude of the force on the particle:

    [itex]F=\frac{q*v*μ_{0}*i*sin(θ)}{2\pi{r}}[/itex]

    However this final equation is the part I am not confident on. I've proceeded on the basis the the magnetic field around an infinite wire carrying current is non-uniform; that is the direction of the magnetic field is not constant, but would appreciate my working being checked!

    Thanks in advance!
     
    Last edited: Feb 21, 2013
  2. jcsd
  3. Feb 20, 2013 #2

    mfb

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    Re: Calculate the force on a particle from magnetic field of infinite

    The magnetic field is not constant, this will change sin(θ) and r in a trajectory. But the equation for the force at a specific radius with a specific angle is correct.
    Current is written with a capital I. "i" is usually the imaginary unit.
     
  4. Feb 20, 2013 #3

    rude man

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    Re: Calculate the force on a particle from magnetic field of infinite

    Looks good.

    BTW i = √(-1) is only for physicists.

    Real men (engineers) use j = √(-1) and i is very regularly used to denote current :smile:
     
  5. Feb 20, 2013 #4

    mfb

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    Re: Calculate the force on a particle from magnetic field of infinite

    And mathematics as well.
     
  6. Feb 20, 2013 #5

    rude man

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    Re: Calculate the force on a particle from magnetic field of infinite

    Yeah, but not real men (and women)! :smile:
     
  7. Feb 20, 2013 #6
    Thanks both! Just needed that extra pair of eyes to look at it :smile:
     
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