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Can someone explain this to me?

  1. Jan 28, 2004 #1
    The force acting on a moving charge particle with mass m and charge q in a magnetic field B is the Lorentz force F= q(v x B), where v is it's velocity. Suppose thata particle moves in the (x,y) plane with a uniform B field in the z direction. Assuming Newton' second law, mdv/dt = F, show that the forceand velocity are perpendicular, and that both have constan magnitude. Hint: Find (d/dt)(v dot v).


    I don't know where to start. How do you take the derivative of v dot v?
     
  2. jcsd
  3. Jan 28, 2004 #2

    HallsofIvy

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    I suspect this will be moved to the "homework" section!

    You differentiate v dot v using the "product rule":

    The derivative of v dot v is: dv/dt dot v+ v dot dv/dt. Since the dot product of vetors is commutative, this is the same as 2v dot dv/dt (should remind you of the derivative of v2).

    Since you are told that "the Lorentz force F= q(v x B)
    "mdv/dt = F" becomes m dv/dt= q(v x B)
     
  4. Feb 1, 2004 #3
    personaly

    I think you should take the dot product first, then take the derivative....it is easier to see what is being done and the algebra is simpler.
     
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