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Magnetic Force in a Current Carrying Wire

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data

    The current in a wire consists of n electrons per unit volume moving with a velocity v. What is the effect on these electrons of the magnetic field set up by the current itself within the wire? What is the force on one electron at a distance r from the centre of the wire?


    2. Relevant equations

    F = QvBsinθ
    Magnetic field strength at a distance r from the axis of the wire outside the wire = u0I/2∏r

    3. The attempt at a solution

    I know that for part 1, the effect of the magnetic field on the electrons inside the wire will be a radially outward force (taking all electrons to be travelling in straight lines along the wire).

    Part 2

    F will be equal to QvBsin90 = QvB

    Making the subsitution for B I have

    F = Qvu0I/2∏r

    I believe now that I have to make subsitution for I. Which would be 4/3∏a3vne

    where e is fundamental charge and a is the radius of the wire.

    This gives:

    F = (3/8)u0ve2na3r

    I know that the answer is:

    F = (1/2)u0v2e2nr
    I think I'm making a mistake in calculating my current, but I'm not sure. Help Please?

    Thanks
     
    Last edited: Mar 14, 2012
  2. jcsd
  3. Mar 15, 2012 #2
    Hi! This is my first time helping someone out so here goes:

    To make the substitution for current I, you should use:
    [itex] I=\int J \bullet da [/itex]
    where J is the current density, equal to nev in this case. After doing a quick integration you should get the proper current which will give the correct answer for the force.
     
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