ELECTRIC FIELD LINES ARE CONTINUOUS CURVES.THEY REPRESENT THE PATH FOLOWED BY A UNIT POSITIVE CHARGE IN AN ELECTRIC FIELD PRODUCED BY A SOURCE CHARGE.IF THEY WOULD HAVE BREAKS THEN THE PATH FOLLOWED BY THE CHARGED BODY WILL BE DISCONTINUOUS BUT PATH OF A CHARGED BODY IS ALWAYS CONTINUOUS IN AN ELECTRIC FIELD. SECONDLY IF ELECTRIC FIELD LINES ARE DISCONTINUOUS THEN IT WILL REPRESENT THAT THE CHARGED BODY HAS JUMPED IN ELECTRIC FIELD FROM ONE POINT TO ANOTHER WHICH IS NOT POSSIBLE. SO ELECTRIC FIELD LINES ARE ALWAYS CONTINUOUS , THEY COULD NOT HAVE BREAKS.