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Magnetic field of Earth, corresponding current

  1. Oct 22, 2011 #1
    1. The problem statement, all variables and given/known data
    Assuming the earth is spherical, and radius is 6371km. At the north pole the magnetic field (caused by a magnetic dipole) points downward with magnitude 62μT.
    a) Calculate the magnetic moment m
    b) Which current I should flow around equator to get a corresponding dipole moment.

    2. Relevant equations
    Amperes Law
    [itex]B_{dip} = \dfrac{\mu_0}{4\pi r^3}(3(\vec{m}\cdot \hat{r})\hat{r}-\vec{m})[/itex]
    Mabye: [itex]\vec{m} = I\int d\vec{a}[/itex]
    3. The attempt at a solution
    a)
    [itex]B_{dip} = \dfrac{\mu_0}{4\pi r^3}(3(\vec{m}\cdot \hat{r})\hat{r}-\vec{m})[/itex]
    m and r points in opposite directions and the problem reduces to:
    [itex]\vec{m} = -\dfrac{\vec{B}_{dip}\pi r^3}{\mu_0}\hat{z}[/itex]
    b)
    I suppose i could use Amperes Law or Biot Savarts law mabye, but i can't see if this compromises the multipole expansion?
     
  2. jcsd
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