  A simple method to calculate the static electric polarization of
single-walled carbon nanotube (SWNT) is obtained within the second-order
perturbation approximation. The results are in agreement with the previous
calculation within the random-phase approximation. We also find that the low
energy electronic band structure of SWNT can be affected by an external
electric field perpendicular to the axis of the tube. The field-induced energy
gap shows strong dependence on the electric field and the size of the tubes,
and a metal-insulator transition is predicted for all $(n, n)$ tubes. Universal
scaling is found for the gap as function of the electric field and the radius
of SWNTs. The fact that the external field required to induce a 0.1 ${\rm eV}$
gap in SWNTs can be reached under the currently available experimental
conditions indicates a possibility of further applying nanotubes to electric
signal-controlled nanoscale switching devices.
