Context : Theoretical arguments indicate that close-in terrestial exoplanets may have weak magnetic fields . As described in the companion article ( Paper I ) , a weak magnetic field results in a high flux of galactic cosmic rays to the top of the planetary atmosphere . Aims : We investigate effects that may result from a high flux of galactic cosmic rays both throughout the atmosphere and at the planetary surface . Methods : Using an air shower approach , we calculate how the atmospheric chemistry and temperature change under the influence of galactic cosmic rays for Earth-like ( N _ { 2 } -O _ { 2 } dominated ) atmospheres . We evaluate the production and destruction rate of atmospheric biosignature molecules . We derive planetary emission and transmission spectra to study the influence of galactic cosmic rays on biosignature detectability . We then calculate the resulting surface UV flux , the surface particle flux , and the associated equivalent biological dose rates . Results : We find that up to 20 % of stratospheric ozone is destroyed by cosmic-ray protons . The effect on the planetary spectra , however , is negligible . The reduction of the planetary ozone layer leads to an increase in the weighted surface UV flux by two orders of magnitude under stellar UV flare conditions . The resulting biological effective dose rate is , however , too low to strongly affect surface life . We also examine the surface particle flux : For a planet with a terrestrial atmosphere ( with a surface pressure of 1033 hPa ) , a reduction of the magnetic shielding efficiency can increase the biological radiation dose rate by a factor of two , which is non-critical for biological systems . For a planet with a weaker atmosphere ( with a surface pressure of 97.8 hPa ) , the planetary magnetic field has a much stronger influence on the biological radiation dose , changing it by up to two orders of magnitude . Conclusions : For a planet with an Earth-like atmospheric pressure , weak or absent magnetospheric shielding against galactic cosmic rays has little effect on the planet . It has a modest effect on atmospheric ozone , a weak effect on the atmospheric spectra , and a non-critical effect on biological dose rates . For planets with a thin atmosphere , however , magnetospheric shielding controls the surface radiation dose and can prevent it from increasing to several hundred times the background level .