Magnetic fields are the fundamental mechanism by which energy is converted from one form to another in motors, generators and transformers.
First, we are going to look at the basic principle – A current-carrying wire produces a magnetic field in the area around it.
Production of a Magnetic Field
1. Ampere’s Law – the basic law governing the production of a magnetic field by a current:
where H is the magnetic field intensity produced by the current Inet and dl is a differential element of length along the path of integration. H is measured in Ampere-turns per meter.
2. Consider a current-carrying conductor is wrapped around a ferromagnetic core;
3. Applying Ampere’s law, the total amount of magnetic field induced will be proportional to the amount of current flowing through the conductor wound with N turns around the ferromagnetic material as shown. Since the core is made of ferromagnetic material, it is assume that a majority of the magnetic field will be confined to the core.
4. The path of integration in Ampere’s law is the mean path length of the core, lc. The current passing within the path of integration Inet is then Ni, since the coil of wires cuts the path of integration N times while carrying the current i. Hence Ampere’s Law becomes,
5. In this sense, H (Ampere turns per metre) is known as the effort required to induce a magnetic field. The strength of the magnetic field flux produced in the core also depends on the material of the core. Thus,
B = magnetic flux density (webers per square meter, Tesla (T))
µ= magnetic permeability of material (Henrys per meter)
H = magnetic field intensity (ampere-turns per meter)
6. The constant µ may be further expanded to include relative permeability which can be defined as below:
7. Hence the permeability value is a combination of the relative permeability and the permeability of free space. The value of relative permeability is dependent upon the type of material used. The higher the amount permeability, the higher the amount of flux induced in the core. Relative permeability is a convenient way to compare the magnetizability of materials.
8. Also, because the permeability of iron is so much higher than that of air, the majority of the flux in an iron core remains inside the core instead of travelling through the surrounding air, which has lower permeability. The small leakage flux that does leave the iron core is important in determining the flux linkages between coils and the self-inductances of coils in transformers and motors.
9. In a core such as in the figure,
Now, to measure the total flux flowing in the ferromagnetic core, consideration has to be made in terms of its cross sectional area (CSA). Therefore,
Where: A – cross sectional area throughout the core
Assuming that the flux density in the ferromagnetic core is constant throughout hence constant A, the equation simplifies to be:
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