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Theoretical Mechanics

  1. Aug 29, 2005 #1
    So I'm stuck on the second part of this problem and really don't know hwere to go from here... let me type it up and show where I got stuck at.

    3. The motion of particle of chage q in an electromagnetic field is governed by the Lorentz force (for low velocities v<<c): F=qE + qvxB.
    With both constant B=B k and E=Ey j + Ez K show that:

    I did F=qE+qVxB=m (dv/dt)

    dvx/dt= q/m(vyBz)
    dvy/dt= q/m(Ey-vxBo)
    dvz/dt= q/m (Ez)

    I think I'm suppose to now take a second derivative and find the second order differential equation but I'm not too sure how to approach that.
  2. jcsd
  3. Aug 30, 2005 #2


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    One slight error here: the strength of the magnetic field is just "B", not
    "Bz" or "Bo".

    What you are "supposed" to do is solve those equations. Since the last one (for dvz/dt) does not involve the other two components, you can solve it directly. The other two are "entwined". One method of solving a pair of equations is to differentiate the first (so that you have dvy/dt on the right side) and then replace dvy/dt from the second equation. That will give you one second order differential equation for vx/
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