We show that the geomagnetic field is more prone to disturbances around the June solstice than around the December solstice, as evidences from a larger enhancement in geomagnetic activity indices ap, an, and as, following the onset of transient solar disturbances occurring in the three-month period around June solstice than in the interval around the December solstice. Further, an asymmetry between the northern and southern hemisphere geomagnetic activity is shown to exist, indepedent of the level of the activity. This asymmetry, represented by (an--as)/ (an+as)/2 shows a regular annual variation with a maximum of 60% around June solstice and is almost absent around the December solstice.