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Magnetic field problem

  1. Mar 31, 2005 #1
    I don't even know where to begin here, could use a hint =/

    "Two positive ions having same charge q but different masses, m1 and m2, are accelerated horizontally from rest through a potential difference V. They then enter a region where there is a uniform magnetic field B normal to the plan of the trajectory. Show that if the beam entered the magnetic field along the x-axis, the value of the y-coordinate for each ion at any time t is approximately y=Bx^2(q/8mV)^1/2 provided y remains much smaller than x. "
     
  2. jcsd
  3. Apr 2, 2005 #2

    Andrew Mason

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    You would use the Lorentz force equation:

    [tex]\vec F = ma\hat j = q v\hat i \times B\hat k = qvB\hat j[/tex]

    Determine speed v from [tex]qV = E = \frac{1}{2}mv^2[/tex]

    Since a is in the direction perpendicular to v, it is in the direction of the y axis. So the distance moved in the y direction is

    [tex]y = \frac{1}{2}at^2[/tex]

    and t = x/v

    That should enable you so solve this problem.

    AM
     
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