In one of Du Moncel's papers on electromagnets[1] you will also find a
discussion on armatures, and the best forms for working in different
positions. Among other things in Du Moncel you will find this paradox:
that whereas using a horseshoe magnet with fat poles, and a flat piece
of soft iron for armature, it sticks on far tighter when put on
edgeways; on the other hand, if you are going to work at a distance,
across air, the attraction is far greater when it is set flatways. I
explained the advantage of narrowing the surfaces of contact by the
law of traction, B², coming in. Why should we have for action at a
distance the greater advantage from placing the armature flatway to
the poles? It is simply that you thereby reduce the reluctance offered
by the air gap to the flow of the magnetic lines. Du Moncel also tried
the difference between round armatures and flat ones, and found that a
cylindrical armature was only attracted about half as strongly as a
prismatic armature having the same surface when at the same distance.
Let us examine this fact in the light of the magnetic circuit. The
poles are flat. You have at a certain distance away a round armature;
there is a certain distance between its nearest side and the polar
surfaces. If you have at the same distance away a flat armature having
the same surface, and, therefore, about the same tendency to leak, why
do you get a greater pull in this case than in that? I think it is
clear that if they are at the same distance away, giving the same
range of motion, there is a greater magnetic reluctance in the case of
the round armature, although there is the same periphery, because,
though the nearest part of the surface is at the prescribed distance,
the rest of the under surface is farther away; so that the gain found
in substituting an armature with a flat surface is a gain resulting
from the diminution in the resistance offered by the air gap.
[Footnote 1: "La Lumiere Electrique," vol. ii.]