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The mechanism of single-walled carbon nanotubes (SWCNTS)aligning in the direction of exteal electric field is studied by quantum mechanics calculations.The rotational torque on the carbon nanotubes is proportional to the difference between the longitudinal and transverse polarizabilities and varies with the angle of SWCNTs to the exteal electric field.The longitudinal polarizability increases with second power of length,while the transverse polarizability increases linearly with length.A zigzag SWCNT has larger longitudinal and transverse polarizabilities than an armchair SWCNT with the same diameter and the discrepancy becomes larger for longer tubes.