What is the relation between force and the air gap length in the flat-faced armature type?

In the context of magnetic circuits, such as those found in electric motors, generators, and similar devices with a flat-faced armature type, the force exerted by the magnetic field on the armature is inversely related to the square of the air gap length. This relationship is derived from the general principle that the magnetic force between two magnetic bodies is proportional to the gradient of the magnetic field, which, in turn, depends on the characteristics of the magnetic circuit, including the air gap.

The mathematical representation often used to describe the force (F) acting on the armature in such a system is derived from the magnetic energy stored in the system or from the magnetic pressure concept. The force can be modeled by the equation:

[ F = frac{{B^2 cdot A}}{{2 mu_0}} ]

where:

– (B) is the magnetic flux density in the air gap,

– (A) is the cross-sectional area of the air gap,

– (mu_0) is the permeability of free space (a physical constant).

Since the magnetic flux density (B) is inversely related to the length of the air gap (l) (due to the magnetic circuit’s reluctance, which increases with the air gap length), the force decreases as the air gap length increases. Specifically, the relationship between the flux density (B) and air gap length can be more complex in practical applications and requires consideration of the entire magnetic circuit, but the fundamental principle is