A brief discussion on magnetic leakage, also introducing the leakage coefficient
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
Key facts In a magnetic circuit, the magnetic leakage can be described using the leakage coefficient, which can be obtained by dividing the sum of the useful and leakage flux, to the useful flux.
Magnetic leakage can be defined as the passage of magnetic flux outside the path along which it can do useful work. The passage of useful and leakage magnetic fluxes is diagramed in Figure 1.
In such conditions, we can define the leakage coefficient as:
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Example - Magnetic flux and flux density of a toroid with an air gap
Consider a toroid with the mean length of , and the cross section of , which also contains an air gap of length . Calculate the number of ampere-turns () which would give a magnetic flux of , and also calculate the magnetic flux density in the iron, if the leakage coefficient for the gap is . The curve for iron is given in Figure E1:
Given that the cross section of the toroid is (), the magnetic flux density in the gap should be: 2) corresponds to: 1), and , we get the required ampere-turns for the air gap: 4) and (5), we obtain the total required ampere-turns for the toroid with an air gap: