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Homework Help: Motion of charged particle in a magnetic field

  1. Sep 21, 2006 #1
    OK first off here is the problem.

    problem: A positive point charge q of mass m is injected with a velocity [tex]u_0 = \mu_0 j[/tex] into the y > 0 region where a uniform magnetic field [tex]B = B_0 i[/tex] exists. Obtain the equation of motion of the charge, and describe the path that the charge follows.

    i, j and k represent unit vectors in the direction of the x, y and z axes.

    Now I understand that the path will be a semicircle from the theory of the motion of a charged particle in a uniform magnetic field and since y > 0 and I know that the force experienced by the particle will be in the z direction.

    [tex]F_m = q(u_0 X B) = q \mu_0 B_0 k[/tex]

    The velocity is going to be constant, but the motion will vary with time in the z direction I think? Obviously my problem is that I'm not too sure of how to solve for the equation of motion in this problem. I guess one of the reasons why I'm finding this so difficult is I can't even visualise it properly.

    Any help to put me on the right track would be great.


    EDIT: I can get the answer by simply equating the centripetal and magnetic forces and then substituting [tex]R= \frac {m \mu_0} {q B_0}[/tex] into the general equation of a semicircle, but I don't think this is how they want you to do it.
    Last edited: Sep 21, 2006
  2. jcsd
  3. Sep 22, 2006 #2


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    Staff Emeritus
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    [tex]u_0 = \mu_0 j[/tex] That's the initial velocity when it enters the magnetic field.

    The velocity does not remain in the j-direction though. The particle accelerates, i.e. changes direction.

    If the 'speed' is constant, what can one say about the trajectory?

    If it leaves the magnetic field, it will travel in a straight line in the direction of the velocity vector where it leaves the M field, unless subject some other E or M field, not parallel with the velocity.
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