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Showing particle travels at constant speed (geometry)

  1. Oct 11, 2016 #1
    1. The problem statement, all variables and given/known data
    the trajectory γ: ℝ→ℝ3 of a charged particle moving in a uniform magnetic field satisfies the differential equation γ''= B x γ'(t) . where B = (B1, B2, B3) is a constant 3-vector describing the magnetic field, and × denotes the vector product.

    (a) Show that the particle travels at constant speed.
    (b) Show that the component of the particle’s velocity in the direction of the magnetic field B is also constant.
    2. Relevant equations


    3. The attempt at a solution
    Apart from knowing γ'' should =0 I have no idea how to show that, I just need a bump in the right direction on how to start

    Thanks for any help
     
  2. jcsd
  3. Oct 11, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    That is not true. In general, acceleration won't be zero.

    You can find the full trajectory, but you can also show that the magnitude of the velocity is constant without the trajectory. For mathematical reasons, it is easier to show that the squared velocity is constant, which is equivalent to the previous statement.
     
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