Problem 22.37

22.37
We know from equation 22.16 that the magnetic field along the axis of a loop of current is given by
$B = \frac{\mu_{0}IR^{2}}{2(x^{2} + R^{2})^{3/2}}$
in the case of the earth, the distance from the center of the loop, x is just the radius of the earth, R, so we have
$B = \frac{\mu_{0}IR^{2}}{2(R^{2} + R^{2})^{3/2}}$
$B = \frac{\mu_{0}IR^{2}}{(2^{5/2})(R^{3})}$
Plugging in the values for the radius of the earth and $\mu_{0}$, we have that the current is
$I = 2.00 \times 10^{9} A$
and from the right hand rule, we find that it is flowing westward.