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Particle released into electric and magnetic fields perpendicular

  1. Mar 7, 2013 #1
    1. The problem statement, all variables and given/known data
    z+ up with E field, y to the right, x out of the page with B field
    particle released from rest at (0,0,0) with only initial y velocity y=(E/B)t
    or initial y=(E/2B)t

    2. Relevant equations
    can you suggest a good differential equations text?
    y(t)=C1cos(wt)+C2sinwt+(E/B)t+C3
    z(t)=C2cos(wt)-C1sin(wt)+C4
    3. The attempt at a solution
    so particle will move in a linear straight line to the right?

    in the case of particle released from rest it will move in perfect half circle paths to the right? so there is a preservation of the geometry?
     
    Last edited: Mar 7, 2013
  2. jcsd
  3. Mar 7, 2013 #2

    mfb

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    Staff: Mentor

    Only for special values of E and B.

    In general, you can calculate those coefficients C1 to C4 in your equations (they are not differential equations, by the way). Alternatively, you can derive those equations from the differential equation given by the Lorentz force.
    Right/left depends on the sign of E and B.
    What does that mean?
     
  4. Mar 9, 2013 #3
    thanks very much! the geometry of the E and B fields/forces is perpendicular and coplanar and are simply rotated pi/2 clockwise

    so...how do you sketch the graphs of these equations for the case?
    v(0)=(E/2B)y, v(0)=(E/B)(y+z), I can find the centers of the circles and differentiate to find min/max but as sinusoidal functions they have some vague wave graph

    do I just plug in values for 0, pi/2, pi, 3pi/2...?
     
    Last edited: Mar 9, 2013
  5. Mar 9, 2013 #4

    mfb

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    Staff: Mentor

    That is a good idea, indeed.
     
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