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Magnetic Field Does Zero Work

  1. May 15, 2013 #1
    1. The problem statement, all variables and given/known data

    This isn't strictly homework, I'm going over my lecturer's notes before the exam and I don't understand a part of this proof for magnetic fields doing no work.

    This is the second proof he gave, the first being the more standard [itex]\vec{B}\cdot\textit{d}\vec{l}=0[/itex]

    2. Relevant equations

    So in the second proof he does it like this;

    I0bwTNq.png

    I cannot figure out where he gets the factor of a half in the third line, to make the equation come out as change in kinetic energy = 0.
     
  2. jcsd
  3. May 15, 2013 #2

    tiny-tim

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    hi conorordan! :smile:
    product rule

    d(v·v)/dt = v·dv/dt + dv/dt·v = 2 v·dv/dt :wink:
     
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