Optimum permanent-magnet dimensions for repulsion applications

The repulsive force between identical right-circular-cylindrical permanent magnets is calculated, and the ratio of this force to the weight of a magnet is maximized through optimization of magnet size and shape. It is assumed that the magnets are uniformly magnetized along their axes. For magnets of thickness
t
and radius
R
, separated by a distance
2h
, the optimum dimensions are
R = 3.45h
and
t = 2.7h
. For these dimensions, the repulsive magnetic force has the value
2.65 \mu_{0}M^{2}h^{2}
newtons, with the magnetization
M
in At/m and
h
in meters.