Basic Concepts of Magnetic Circuits - your electrical guide
Magnetic Field
The magnetic field of a magnet is defined as the region near the magnet within which the influence of the magnet is felt.
Magnetic Line of Force
The magnetic line of force may be defined as a line along which an isolated N-pole would travel if it is allowed to move freely in a magnetic field. These lines are imaginary and do not have any physical existence. These are used for representing the magnetic field of a magnet.
Magnetic Flux
The magnetic flux is defined as the total number of magnetic lines of force in a magnetic field. It is denoted by φ. It is measured in webers.
1 Weber = 108 lines of force.
Magnetic Flux Density (B)
The flux per unit area is defined as the magnetic flux density. It is measured in a plane perpendicular to flux.
Magnetic Flux Density, B = φ ÷ A  
Units: Weber per meter square (Wb/m2) or tesla(T).
Magnetic Field Intensity
The magnetic field strength or magnetic field intensity is given by MMF per unit length of the magnetic circuit.
Magnetic Field Intensity, H = (NI) ÷
where N = Number of turns of magnetizing coil
              I = Current through the coil
              l = length of magnetic material in meters
Units: AT/m.
The magnetic field intensity is also known as magnetic field strength or magnetizing force.
The ability of a material to carry the magnetic lines of flux is known as permeability of that material.
The magnetic lines of force can pass through high permeability materials like iron, steel, very easily. Low permeability materials like wood etc. don’t allow the flux lines to pass through them easily.
Absolute Permeability
It is the ratio of flux density (B) in a particular medium to the magnetic field strength (H) which produces magnetic flux density. It is denoted by µ.
Absolute Permeability, µ = µo µr
Units: Henry/meter (H/m)
Permeability of the Air/Space/Vacuum
If a magnet is kept in air or vacuum, then the ratio of flux density (B) and magnetic field strength (H) is defined as the permeability of free space. It is denoted by µo.
Permeability of Free Space, µo = 4π x 10-7 H/m
Relative Permeability
The ratio of permeability of material to the permeability of vacuum or air is known as relative permeability.
Relative Permeability, µr = µ ÷ µo
It has no units.
The relative permeability of vacuum, air and all non-magnetic materials is 1. The relative permeability of all the magnetic materials is very high. For example, the relative permeability of permalloy (nickel 78% and iron 22%) is about 50000.
Magneto-motive Force (MMF)

Magneto-motive Force (MMF)

The magneto-motive force is the driving force which produces the magnetic flux. The magnetic field intensity (H) is decided by MMF.
Magneto-motive Force, MMF = NI
where N = Number of turns of magnetizing coil
            I = Current through the coil
Units: Ampere Turns (AT)
Reluctance (S)
It is opposition offered to the flow of magnetic flux by the magnetic material.
Unit: AT/Wb
Reluctance, S = l ÷ (µ x a)
where l = length of the magnetic path in meters.
           a = area of the cross-section of magnetic path in meter square.
           µ = absolute permeability of medium in H/m.
              = µoµr
Therefore, Reluctance, S = l ÷ (µoµra)
The reluctance is also given by the ratio of the MMF and the amount of flux produced.
i.e. Reluctance, S = MMF ÷ flux
Reluctance, S = (NI) ÷ φ
The permeance of a material represents the ease with which magnetic flux can be produced in that material. It is reciprocal of reluctance. Its unit is Wb/AT or henry.
Leakage Flux
The part of the total magnetic flux which flows through the magnetic circuit is called useful magnetic flux. However, the magnetic flux which does not completely pass through the magnetic path, but partially passes through the air is called leakage magnetic flux.

leakage magnetic flux

Mathematically, φtotal = φuseful + φleakage
Leakage Factor (λ)
The ratio of total flux produced to the useful flux is called leakage factor or leakage coefficient.
Leakage factor,   λ = φtotal / φuseful
The value of leakage factor is always greater than unity. Typical values of leakage factor are from 1.12 to 1.25. In the magnetic circuits, the magnetic leakage can be minimized by placing the exciting coils as close as possible to the points where the flux is to be utilized.
The magnetic lines of force repel each other while passing through a non-magnetic material. Due to this when the flux lines cross the air gap, they tend to bulge outwards. This effect is known as fringing.

magnetic fringing

The effect of fringing is to make the effective air gap area larger than that of magnetic path and consequently, the flux density in the air gap is reduced. The effect of fringing depends upon the length of the air gap. To minimize fringing, the air gap length is kept as small as possible. The effect of fringing can be neglected if air gap length is very small as compared to its width.

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