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Homework Help: Point Particle in Magnetic Field

  1. May 9, 2006 #1
    Hey, Guys!

    Could you please give me some guidance for the following problem:

    A point particle of mass m and charge q moves with an arbitrary initial velocity [itex]\vec{v}[/itex] in constant magnetic field [itex]\vec{B}[/itex]. The point particle is moving under the influence of the Lorentz-force:[itex]\vec{K}=\frac{q}{c}(\vec{v}\times\vec{B})[/itex], where c - speed of light. Evaluate the path:[itex]\vec{r}(t)[/itex]

    Where or how should I start? Just ask me guiding questions, please.

    Thanks :smile:
    Last edited: May 9, 2006
  2. jcsd
  3. May 9, 2006 #2
    We formulate the law of motion as ODE:
    [itex]m\vec{a}=\frac{q}{c}(\vec{v}\times\vec{B})[/itex], where of course [itex]\vec{a}=\ddot\vec{r},\vec{v}=\dot\vec{r}[/itex] So all we have to do is to solve this ODE. But how do we handle the cross-product in an ODE?
    Last edited: May 9, 2006
  4. May 9, 2006 #3
    I'm not sure but maybe you should write the cross product in the matrix determinant form.
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