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Force on electron travelling parallel to charge carrying longstraightwire

  1. Jul 26, 2012 #1
    1. The problem statement, all variables and given/known data

    An infinitely long straight wire of radius a = 0.01m carries a total current I = 1A
    uniformly distributed over the area of the wire. An electron with instantaneous velocity (at time t ) v = 1000ms directed parallel to the wire (in the same direction as I ) is r = 0.1m away from the wire centre. What are the magnitude and direction of the force acting on the electron at time t due to the magnetic field B produced by the current?

    2. Relevant equations

    F=qV x B

    3. The attempt at a solution

    F=qV x B
    =qvBsinθ
    =qvB

    B=μ0I/2∏r

    My question is how to handle the radii? Would you calculate from the centre of the wire or the surface of the wire?

    And in regards to the direction of the force if v is along the paper B would be into it and F would be down it.

    Does this all seem correct?
     
  2. jcsd
  3. Jul 26, 2012 #2
    First off, the electron will be directed in a helix around the wire moving parallel to the wire at a rate of 1000 m/s. The helix motion is caused by the magnetic force and the centrifugal force's equivalence. The direction of the force has to be perpendicular to the wire if you use the hand rule since the magnetic field around a wire is circular. The formula I would use to calculate the force is:

    F = Bqv

    The charge of an electron is 1.6*10-19

    Of course you have to find the magnetic field before you can use this equation. The equation that you listed will work.

    [itex]\frac{μ_{0}I}{2πR}[/itex]

    The permeability of free space (μ0) is about 4π*10-7 TmA-1
    Use the radius given. The circumference of the wire is assumed to be negligible.
     
    Last edited: Jul 26, 2012
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