Ion and electron drifts (earth's magnetic field)

(F. F. Chen ~ 2.8) Suppose the earth's magnetic field is \(3\times10^{-5}\) T at the equator and falls off as \(1/r^3\) as in a perfect dipole. Let there be an isotropic population of 1 eV protons and 30 keV electrons, each with density \(n=10^7$ m$^{-3}\) at \(r=5\) earth radii in the equator plane.

(a) Compute the ion and electron \(\vec{\nabla} B\) drift velocities.

(b) Does an electron drift eastward or westward?

(c) How long does an electron take to encircle the earth?

(d) Compute the current ring density in A/m\(^2\).