Muon Charge Information from Geomagnetic Deviation in Inclined Extensive Air Showers

We propose to extract the charge information of high energy muons in very inclined extensive air showers by analyzing their relative lateral positions in the shower transverse plane. We calculate the muon lateral deviation under the geomagnetic field and compare it to dispersive deviations from other causes. By our criterion of resolvability, positive and negative muons with energies above $10^4$ GeV will be clearly separated into two lobes if the shower zenith angle is larger than $70^\circ$. Thus we suggest a possible approach to measure the $\mu^+ / \mu^-$ ratio for high energy muons.