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What is Leakage Flux and Fringing in Magnetic Circuits?
Magnetic Leakage or Leakage Flux
The part of magnetic flux that does not follow the desired path in a magnetic circuit is known as leakage flux.
In most of practical magnetic circuits, the path of a large part of the magnetic flux is through iron part of the magnetic circuit and the rest part of magnetic flux flows through air. The magnetic flux in the air gap is known as useful flux $(\varphi_{g})$ since it can be used for various useful purposes.
Consider a magnetic circuit having an iron core with a coil wound on it and having a narrow air gap. The total magnetic flux produced by the coil does not pass through the air gap i.e. some part of it leaks through the air surrounding the iron core (see the figure), this magnetic flux is called as leakage flux (ϕleakage).
Let,
$$\mathrm{Total\: magnetic\: flux \:produced\: or \:flux \:in \:iron core =\varphi_{i}}$$
$$\mathrm{Useful \:magnetic\: flux\: in\: air\: gap =\varphi_{g}}$$
$$\mathrm{\therefore\:Leakage \:Flux,\varphi_{leakage}=\varphi_{i}-\varphi_{g}}$$
Also, the leakage coefficient for a magnetic circuit is given by,
$$\mathrm{Leakage\: Coefficient,\lambda=\frac{Total \:Magnetic\: Flux(\varphi_{i})}{Useful\: Magnetic\: Flux(\varphi_{g})}}$$
The value of the leakage coefficient (λ) for electrical machines is usually ranges from 1.15 to 1.25.
Important − The magnetic leakage or leakage flux is undesirable in electrical machines because it increases the weight and cost of the machine.
Magnetic Fringing
When the magnetic field lines pass through an air gap, they tend to bulge out (see the above figure). It is because the magnetic field lines repel each other when passing through the air (or non-magnetic materials). This effect is known as magnetic fringing.
Due to magnetic fringing, the effective area of the air gap is increased and thus the magnetic flux density is decreased in the air gap. The longer the air gap, the higher is the fringing and vice-versa.
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