Magnetic Pull Force
An analysis of the magnetic pull force which arises between the poles of an electromagnet
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
Key facts For an electromagnet characterized by the area , the magnetic flux density , and the relative magnetic permeability , the magnetic pull force is:
where is the magnetic permeability of free space. <br/> Constants
Consider an electromagnet of area and magnetic flux density , and also imagine a displacement of as highlighted in Figure 1. We know that the energy stored in a magnetic field of no magnetic saturation is given by: Stored Energy ). Thus, the change in energy stored following the displacement will be: 4) and (5), we get that:
Example - Magnetic pull force of an electromagnet
Consider the electromagnet diagramed in Figure E1, characterised by the lengths , , and , and the area . Given that a current of passes through a coil with turns and relative magnetic permeability of , find the total magnetic pull force.
We know that the total magnetic reluctance of a magnetic circuit of length , cross-sectional area , and relative magnetic permeability , with an air gap of length , is given by: 3), we obtain from (4) and (5) that the total magnetic flux is: 6) and that (), we obtain the magnetic flux density in the air gap: 8), and that (), and the relative magnetic permeability of air is , the magnetic pull per pole becomes: