  The rare event search experiments using germanium detectors are performed in
the underground laboratories to prevent cosmic rays. However, the cosmogenic
activation of the cupreous detector components on the ground will generate long
half-life radioisotopes and contribute continually to the expected background
level. We present a study on the cosmogenic activation of copper after 504 days
of exposure at an altitude of 2469.4 m outside the China Jinping Underground
Laboratory (CJPL). The specific activities of the cosmogenic nuclides produced
in the copper bricks were measured using a low background germanium gamma-ray
spectrometer at CJPL. The production rates at sea level, in units of
nuclei/kg/day, are 18.6 \pm 2.0 for Mn-54, 9.9 \pm 1.3 for Co-56, 48.3 \pm 5.5
for Co-57, 51.8 \pm 2.5 for Co-58 and 39.7 \pm 5.7 for Co-60, respectively.
Given the expected exposure history of the germanium detectors, a Monte Carlo
simulation is conducted to assess the cosmogenic background contributions of
the detectors' cupreous components.
