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Can someone explain these equations?

  1. Jun 11, 2014 #1
  2. jcsd
  3. Jun 11, 2014 #2

    jedishrfu

    Staff: Mentor

    equation 196 is just saying that v can be written as a vector sum of ExB/b^2 + v'

    the ExB vector is perpendicular to both E and B fields (which in this case are perpendicular to each other)

    and so subbing the expression in for v into equation 195 you get equation 197

    vxB = (ExB/B^2 + v') x B = ExBxB/B^2 + v'xB = v'xB since ExBxB is zero vector.
     
  4. Jun 11, 2014 #3
    Thanks. But why is equation 196 true?
     
  5. Jun 11, 2014 #4

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    If you have any two vectors p and q, you can always write p = q + v'. v' is just p-q.

    The reason for doing this in Eq 196 is because the ExB vector and the v' vector each have different "nice" properties, and after you split up the equation you can work with each vector separately.
     
  6. Jun 11, 2014 #5
    Oh, ok. That makes much more sense. Thanks!
     
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