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Effect of a magnetic field on a bean of particles.

  1. Jan 19, 2009 #1
    1. The problem statement, all variables and given/known data
    a beam of particles of charge q with velocity v is emitted from a point source, roughly parallel with a magnetic field B, but with a small angle of angular dispersion. Show that the effect of the field is to focus the beam to a point at a distance z = 2[/pi]mv/|q|B.


    2. Relevant equations
    We know the force F= q vxB
    dv/dt = -q/m Bxv


    3. The attempt at a solution
    I try to solve the problem with the force. However, since the beam is roughly parallel to B, the cross product tends to 0. I am now like clueless...
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 19, 2009 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    The initial velocity is approximately parallel to B, not exactly parallel. Try calling the angle between v and B, [itex]\theta[/itex] and calculating r(t) for a particle on the beams outer edge. Then use a Taylor approximation for your expression for small [itex]\theta[/itex] to find the location where r(t) lies on the z-axis (assume that B points in the z-direction).
     
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