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Deriving the Magnetic Field from a Magnetic Dipole

  1. Apr 15, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that: ##B=\frac { 1 }{ 4\pi \epsilon r^{ 3 } } \left[ 3\hat { r } \left( \hat { r } \cdot \vec { m } \right) -\vec { m } \right] ##

    2. Relevant equations

    B=delxA, m=a*I

    3. The attempt at a solution

    I follow my professors derivation. However, she expands the term: ##\vec { \nabla } \times \left( \vec { m } \times \vec { r } \right) =2 \vec m## by just using the determinate. I figured I would go with the less messy "BAC CAB" like she uses on another term. However, I can't get ##2 \vec m## by using BAC CAB. I get ##3 \vec m## instead. I have tried both ways using spherical and cartesian. Does not ##\nabla \cdot \vec m=0##? If I can show that ##\vec { r } \left(\vec \nabla \cdot \vec m \right)=-\vec m##. I would be home free, but I think it should equal zero.

    Any E&M or vector calc. gurus, your help would be appreciated.

    Chris Maness
  2. jcsd
  3. Apr 15, 2015 #2


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  4. Apr 15, 2015 #3
    Dang, ok. That was a pretty basic oversight. Thanks

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