Magnetic field of Earth, corresponding current

[dikmikkel]

Homework Statement

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.

Homework Equations

Amperes Law
$B_{dip} = \dfrac{\mu_0}{4\pi r^3}(3(\vec{m}\cdot \hat{r})\hat{r}-\vec{m})$
Mabye: $\vec{m} = I\int d\vec{a}$

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?

 

[_coyote_]

\oint \vec{B} \cdot d\vec{l} = \mu_0 II = \dfrac{1}{\mu_0}\oint \vec{B} \cdot d\vec{l}Any help would be greatly appreciated.