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I Deriving Larmor frequency problem

  1. Jun 21, 2017 #1
    upload_2017-6-22_0-53-7.png
    upload_2017-6-22_0-53-44.png

    I don't get how they get Eq. 5. Why is the direction of ##\mu## going outwards from the direction of B? And why does the fact that ##\frac{d\mu}{dt}## is perpendicular to both ##\mu## and ##B## mean that ##\mu## goes in circle?
     
  2. jcsd
  3. Jun 21, 2017 #2
    All that they are assuming is that ##\vec{\mu}## and ##\vec{B}## are not aligned. If they are aligned, then the equation does not apply, since then the cross product is zero, so that there is no change in ##\vec{\mu}##. But they are assuming that they are not aligned, and that the equation does apply.

    As for why it goes in a circle... Start with two vectors. Call them ##\vec{\mu}## and ##\vec{B}##. Now draw a third, infinitesimal, vector perpendicular to both ##\vec{\mu}## and ##\vec{B}##, call this third vector ##\vec{\delta}##. Form the sum ##\vec{\mu} + \vec{\delta} = \vec{\mu '}##. Now draw another infinitesimal vector perpendicular to ##\vec{\mu '}## and ##\vec{B}##. Add that one to ##\vec{\mu '}## to form ##\vec{\mu ''}##. Keep doing that forever. You'll find that you've drawn a circle.
     
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