One way of qualitatively understanding the flow of charged particles into a pulsar's magnetosphere is to imagine a charged particle of mass m and charge e (the fundamental unit of charge) at the equator of the neutron star. Assume for convenience that the star's rotation carries the charge perpendicular to the pulsar's magnetic field. The moving charge experiences a magnetic Lorentz force of Fm=evB and a gravitational force, Fg. Show that the ratio of these forces is
FgFm=Pmg2πeBR,
where R is the star's radius and g is the acceleration due to gravity at the surface. Evaluate this ratio for the case of a proton at the surface of the Crab pulsar, using a magnetic field strength of 108 T.