Why is magnetism at the center of a bar magnet zero?

The field at the center is not zero, but weak. At the exact center of a magnet the field lines are parallel (straight lines if we draw it). Any where else they are slightly divergent. There is a higher density of field lines at the edges of the poles, and thus a stronger force on the plate Figure A. read more

Secondly, No magnetic force lines come out from or terminate at the center of the bar magnet, all magnetic force lines remain within the bar. So the center remains at zero magnetism. I think this can help. read more

Moreover, the density of the field lines on the picture is maximized at the"poles" of the bar magnet and minimized at the center which means that the magnitude of the magnetic field is smallest at the center, too. It's not hard to see why the field lines look approximately as those on the picture above. read more