If the magnetic field of the Earth fell to zero it would expose the
surface to cosmic radiation - especially the charged particles of the solar wind which are
normally deflected by this magnetic field.
I don't believe that there would be any
substantial effect on the atmosphere except for the occurrence of auroras at many places on
the globe. (Northern Lights – glows in the atmosphere as the particles descend). At present
this is only observable at high latitudes.
Because of the absorbing affect of the
atmosphere most of these charged particles would be absorbed before they reached the
ground and so would have little effect on the vegetation.