# Magnetic field of Earth, corresponding current

1. Oct 22, 2011

### dikmikkel

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

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